2373
ELECTRODE PROCESSES WITHOUT SEPARATION OF DOUBLE-LAYER CHARGING
Electrode Processes without a Priori Separation of Double-Layer Charging
by Paul Delahay Department of Chemistry, N e w York University, N e w Y o r k , N e w York
10003
(Ebeceiued February 9 , 1966)
A priori separation of faradaic and double-layer charging currents, as commonly accepted, is not justified theoretically for nonsteady-state conditions (transients or periodic variations). The idea of charge separation or recombination at an interface, without external current, is introduced and applied to the analysis of charging processes. There can be progressive transition in double-layer charging from the ideal polarized electrode (no charge separation or recombination) to the ideal reversible electrode (only charge separation or recombination). Unawareness of this idea vitiates some results obtained by relaxation or perturbation methods in electrode kinetics. Three general equations are derived which, after solution for any particular conditions, describe nonsteady-state electrode behavior and allow a posteriori determination of kinetic and double-layer parameters. Application is made to an electrode of varying area at constant overvoltage.
It is customary to derive faradaic currents for nonsteady conditions (transients or periodic variations) by ignoring double-layer charging. Experimental currents are subsequently corrected for double-layer charging by assuming behavior as an ideal polarized electrode. Thus, faradaic and double-layer charging processes are separated a priori. This procedure was refined recently, and methods were developed to separate the faradaic and charging processes from their differences in time or frequency dependence. (a) Sluyters and co-workers' devised a method for the analysis of electrode impedance measurements by assuming that the charging process is frequency independent, whereas the faradaic impedance is generally not. (b) Butler and Meehan2 and independently the writer and co-workers3 attempted separation of faradaic and charging currents a t a dropping liquid metal (mercury, amalgam, etc.) electrode from the difference in the time dependence of these two currents. (c) A similar analysis based on dependence on the rate of flow of mercury (amalgam) was devised3 for the streaming mercury electrode. These analyses still presuppose the a priori feasibility of separating faradaic and charging currents. It turns out, as will be shown below, that such a postulate is not justified theoretically and that it can lead to serious errors of interpretation in certain cases. We shall begin with the analysis of two simple cases and shall then derive three general equations
which, after solution for any particular conditions, describe electrode behavior and allow a posteriori separation of kinetic and double-layer parameters. These three general equations should provide the key to the analysis of transitory and periodic electrode processes. Finally, we shall examine the application to an electrode of varying area a t constant overvoltage. Analysis of the faradaic impedance has also been ~ornpleted,~ and other methods (potentiostatic, galvanostatic, etc.) are being analyzed.
Charging Processes at a Metal Ion-Pure Metal Electrode Ionic Transfer vs. Charge Separation or Recombination. We examine charging processes a t an electrode of pure metal M in a solution of salt MX. The electrode reaction is M + E ze = 11 with z > 0. The electrode area A is varied, and the electrode potential is maintained, e.g., by a potentiostat, a t the equilibrium value corresponding to the bulk activity of MX. Such idealized conditions can actually be closely approximated, e.g., for an expanding mercury drop in
+
(1) M. Sluyters-Rehbach and J. H. Sluyters, Rec. Trav. Chim., 82, 525 (1963). See the same journal for previous and more recent papers in this series. (2) J. N. Butler and M. L. Meehan, J. P h y s . Chem., 69,4051 (1965). (3) G.Tessari, J. Murphy, R. de Levie, and P. Delahay, Louisiana State University, unpublished work. (4) P. Delahay and G. G. Susbielles, J. Phya. Chem., in press.
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PAULDELAHAY
2374
a Hg(1) s ~ l u t i o n . We ~ ~ ~shall assume here and in subsequent developments that solutions (and amalgams) are sufficiently dilute so that absolute and relative surface excesses are equal for all practical purposes.6 This condition is generally satisfied in practice. There are two processes by which ions M+z needed to maintain the equilibrium surface excess J?+ of M+I in solution are supplied to or removed from the double layer, as the electrode area varies: (a) transfer of M+zto or from the bulk of the solution; (b) charge recombination or separation at the interface by the reaction M f Z ze = M. The charges on the electrode and in the double layer always remain equal and of opposite sign. Hence, the transfer of an ionic charge (zFI'+)6A from or to the bulk of the solution, which results from a variation 6A, requires addition to or removal from the electrode of an electronic charge - (zFr+)6A. Current flows in the external potentiostat-cell circuit in this operation. In contrast, charge recombination or separation at the metal-electrolyte interface by the process M+I ze = M does not require an external current.6 For instance, dissolution of r+6A moles of M+* produces an ionic charge (zFF+)6A in the double layer and leaves an equal electronic charge of opposite sign on the electrode. The charging current being measured thus depends on the relative contributions of two processes, and recognition of the possibility of charge separation or recombination without a n external current i s the key idea of this paper. Charging Currents. We calculate the charging currents for the above processes on the assumption that only one charging process is to be considered. We also assume that the double layer is at equilibrium with respect to the ionic concentrations just outside the diffuse double layer. I n the absence of supporting electrolyte, the charging current (not the current density) for supposedly pure ionic transfer is
+
+
I
=
zF(r-
- r+>(dA/dt)
(1 )
where I'- is the surface excess of X- and z > 0. A positive current indicates transfer of a positive charge from the potentiostat to the electrode of varying area through the wire connected to the electrode. Since the charge density on the electrode is q =
--zF(r+-
r-)
(2)
one has
I = q(dA/dt)
(3)
Thus, the charging current is proportional to the charge density on the electrode, just as for an ideal polarized T h e Journal of Physical Chemistry
electrode. This conclusion also holds for a solution with supporting electrolyte. The charging current for supposedly pure charge separation or recombination is, in the absence of supporting electrolyte
I
= zFr-(dA/dt)
(4)
where z > 0. In view of eq 2 one has
I
= (4
+ zFI?+)(dA/dt)
(5)
+
The charging current is proportional to p zFI'+, and this result also holds in presence of a supporting electrolyte. The quantity q zFr+ is precisely the one which is obtained by thermodynamic analysis of an ideal reversible e l e c t r ~ d e . ~Thus, ?~ charge separation or recombination is the sole process supplying or removing ions M+I for an ideal reversible electrode. This is understandable since such an electrode must have, by definition, an exchange current density i o approaching infinity for any dynamic conditions of measurement. Hence, any driving force, no matter how small, will cause charge separation or recombination. The driving force, in the above example, is the vanishingly small overvoltage resulting from the vanishingly small gradient in the concentration of ions M f Zat the electrode. This gradient is caused by a vanishingly small contribution of ionic transfer to the charging process. Conversely, only ionic transfer of M+I is operative when io+ 0, and behavior as an ideal polarized electrode prevails. These two behaviors are only limiting cases of the more general situation in which both ionic transfer and charge separation or recombination contribute to double-layer charging. The validity of considering only the limiting cases depends entirely on the relative contributions of the above two processes, i.e., on experimental conditions. The current practice of using the charging current for an ideal polarized electrode should be nearly correct for sufficiently low io values. Conversely, the charging current for an ideal reversible electrode should be used for sufficiently high iovalues, but this has not been done. A general treatment is
+
( 5 ) This matter was called to the author's attention by Dr. R. de Levie of Georgetown University, Washington, D. C. (6) We neglect the displacement currents corresponding to movement of charges from the interface to the double layers in the metal and solution. These displacement currents are negligible in comparison with the current for ionic transfer in the bulk of the solution. The necessity of considering displacement currents was called t o the author's attention by Dr. J. R. Macdonald of Texas Instruments, Dallas, Texas. (7) D. C. Grahame and R. B. Whitney, J. Am. Chem. Soc., 64, 1548 (1942). (8) D. M. Mohilner, J . Phys. Chem., 66, 724 (1962).
ELECTRODE PROCESSES WITHOUT SEPARATION OF DOUBLE-LAYER CHARGING
2375
needed because there is no criterion to determine which charging current must be used and, in many instances, neither of these limiting values can be used because of the simultaneous contribution by ionic transfer and charge separation or recombination. Furthermore, the relative extent of these two contributions is time or frequency dependent, and the treatments of nonsteady-state processes have to be reexamined because they presuppose that the differential capacity of the double layer is constant. The resulting error can be quite serious in certain cases.
supply because part of if is used up in charge separation or recombination. Thus if, as given by the usual equations of electrode kinetics, is not a measurable quantity in nonsteady-state conditions. Both contributions of ionic transfer and charge separation or recombination are included in eq 6 but cannot be separated. It is only by solving the mass-transfer problem that one can calculate if in terms of the activities of reactants and products at the interface. The second equation relates the continuity of fluxes a t the interface with the variations of I?+ and I ' M . Thus
Three General Equations for Nonsteady-State Electrode Processes
(7) where the flux V M of M is taken as positive from the bulk of the amalgam toward the interface.1° The third equation gives the current density being measured, i, in terms of the flux v+ (which is derived by solution of the mass-transfer problem for the boundary conditions of eq 6 and 7). Thus UM
We now show that faradaic and charging processes obey a set of three general equations for nonsteadystate conditions. These equations will be written first for metal ion-amalgam electrodes and afterwards for other types of electrode processes. The electrode area in this section is supposed to be constant. (The electrode of varying area is treated as an application a t the end of the paper.) It is assumed that the double layer is always a t equilibrium with respect to the activities just outside the diffuse double layer. Metal Ion-Amalgani Electrodes. We consider the reaction M+z ze = M(Hg) and neglect the thicknesses of the double layers in the solution and metal (no displacement current of the type discussed in footnote 6). The amalgam-electrolyte interface thus is regarded, as far as mass transfer is concerned, as a plane on which are accumulated the ionic surface excesses, r M of the neutral metale M, and the electronic charge density q. This simplification is justified since the thicknesses of the solution and metal double layers are negligible in comparison with diffusion layer thicknesses for lcI+z and 31 for usual electrode kinetic measurements. This remark holds even for very short measuring times (lO-'sec or even shorter times) or high frequencies. We first write the balance condition for production or at the interface. Thus consumption of i\l+z
+
+
if = ZFU+ zF(dI'+/dt)
(6)
Here if represents the faradaic current density as expressed in terms of the exchange current density, overvoltage, etc. A positive if corresponds to net oxidation, in agreement with our above convention of taking a positive charging current as one supplying a positive charge to the electrode through the wire conin solution is positive nected to it. The flux u+ of Ill+z in the direction from the electrode toward the solution. It must be stressed that not all the current ifflows in the wire connecting the electrode to the external power
= U+
=
+ dr+/dt + dI'M/dt
ZFV+
+ d(q + zFI'+)/dt
(8b)
where the ionic valences zi are taken with their sign and q is the charge density on the electrode. No masstransfer complications are supposed to prevail for all ions except in the writing of eq 8. The summation includes all ions except M+" since the latter has already been counted in eq 6. The summation must be preceded by a minus sign with our convention, as one can readily ascertain by noting that bringing an anion in the double layer requires the supply of a positive current by the external source. Equation 8a is converted to 8b by noting that q is equal to - ZzjFI'j for all ions including M+z. The term zFv+ in eq 8a and 8b corresponds to the total flux of the ions which are consumed or produced a t the interface and accumulated in or removed from the double layer. Solution of the General Equations. Equations 6 and 7 are the boundary conditions for which the masstransfer problem must be solved. The resulting expression for u+ is then introduced in eq 8 and i is obtained. To apply this procedure one must eliminate r + and I'M as unknown functions of time and express them as functions of the potential E of the electrode. The simplest case corresponds to the low overvoltage approximation by which one introduces the (dI'/dE)'s (9) r M is completely equivalent in a formal way to the sum of the surface excess of ions M +r in the metal and the same surface excess of electrons. (10) One can, of course, write eq 6 as if = z F v ~ - - zF(drM/dt) and use Z'M instead of a + . This procedure is completely equivalent to the one followed here.
Volume YO, Number Y
J u l y 1966
2376
a t the equilibrium potential. in eq 6 to 8 are replaced by
PAULDELAHAY
Thus all the (dI’/dt)’s
t = 0.) Conversely, charge separation or recombination should be the only contribution to charging, as far as M+I is concerned, for t + m , and charging as an ideal reversible electrode should prevail. The corresponding differential capacity of the double layer for t + m is not d(q zFI’+)/dE for an amalgam electrode but a somewhat more involved expression because both concentrations of h!I+zand M vary simultaneously. The capacity d(q zFI’+)/dE corresponds to variation of a single concentration, the other concentration remaining constant (see thermodynamics of the ideal reversible electrode’**). Details of the separation of the double-layer parameters must be worked out in each particular condition of mass transfer and cannot be predicted. Corollary thermodynamic study of the electrode from electrocapillary curves appears advisable and possibly essential. I n addition to the above two extrapolations, curve fitting over the whole time or frequency range seems advisable. Computer treatment of data may be necessary and almost essential if the low overvoltage approximation is not justified. An objection may be raised to zero-time or infinitefrequency extrapolation. Thus, the thicknesses of the diffusion layers for M+” and M approach zero for t = 0, whereas our model supposes that these layers are very thick in comparison with the double layers in the amalgam and solution. This contradiction is only apparent because the experimental results, which are extrapolated to time zero, correspond to conditions for which the model is entirely justified. Comparison with the Usual Equations. We compare eq 6 to 8 with the equations usually applied, namely
+
where the subscript q = 0 indicates zero overvoltage. The [(bI’/bE),,o] terms in the resulting modified eq 6 to 8 are then constant coefficients. The expression for if is also simplified in that case since the usual linearized low-overvoltage i us. q characteristic can then be used (although this is not necessary). It should be noted that we express I’ in eq 9 as a function of the single variable E although there are two varying concentrations (of M+” and &I). However, these two concentrations are not independent because the corresponding fluxes are related” by eq 7. This procedure cannot be applied when q is constant (potentiostatic conditions). One then uses one of the concentrations (or AI-+” or hl) as variable. The boundary conditions (6) and (7) become much more cumbersome when the overvoltage variations are so large that the (br/dE)’s a t 0 = 0 cannot be used. It is then necessary to express the (bI’/bE)’s as functions of E . Such functions are, in general, not known a priori, and one is left with the possibility of expanding I’ as a series of E . A quadratic expansion may suffice if the overvoltage interval is not too wide, but, anyhow, boundary value problems become rapidly more involved. This is only a practical difficulty but definitely not a fundamental one. This difficulty militates against the use of nonsteady-state methods involving large overvoltage (although other features may more than compensate the complexity of mathematical analysis). A Posteriori Determination of Kinetic and Double Layer Parameters. We consider the low-overvoltage approximation first. The parameters to be determined a t the equilibrium potential are io, dq/dE, dr+/dE, and dFM/dE. I t is assumed that the diffusion coefficients or any other parameters for mass transfer are determined in separate experiments for pure control by mass transfer or by some other method. The two extrapolations of i against a function of time m (or to infinite and zero frequency, to t = 0 and t respectively) give four relations, namely two slopes and two intercepls. At t = 0, the contribution of charge separation or recombination to charging is negligible for any finite io, i.e., v+ for t = 0 should contain a term which cancels with the term in dr+/dt in eq 8b. It should then lie feasible to obtain io and dq/dE a t the equilibrium potential. (Note that when io+ the ideal reversible electrode behavior prevails even for The Journal of Physical Chemistry
+
if =
zFv+
(104
v+
(lob)
VM =
i = xFv+
+ dq/dt
(10c)
These equations are erroneous for the following reasons : (a) they neglect the double-layer contribution in the expressions for ifand VM; (b) they imply charging as an ideal polarized electrode. Equations 6 to 8 reduce to eq 10 when both dI’+/dt and dI’nf/dt are negligible in comparison with other terms in eq 6 to 8. This condition is quite frequently not fulfilled, even in the absence of specific adsorption of M+zl as one can readily ascertain by calculating dP+/dE from diffuse double-layer data and theory.’* Specific ad(11) This was pointed out by Mr. G. G. Susbielles of this labora-
tory. (12) I n the absence of specific adsorption, one calculates from diffuse double-layer theory zF(dr+ /dE) 5 190 rf cm -* for the following conditions: 10-3 M solution of M+s, z = 2 , 2 5 O , a potential of -0.5
ELECTRODE PROCESSES WITHOUT SEPARATION OF DOUBLE-LAYER CFIARCINQ
sorption should generally render eq 10 even less satisfactory. Other Types of Electrode Processes. Equations 6 to 8 can be transposed to other processes. Metal ionpure metal electrodes can be disposed of immediately since eq 6 and 8 remain, whereas eq 7 is deleted. The limiting cases for t = 0 and t + 03 correspond to a double-layer differential capacity equal to dq/dE and to d(q zFF+)/dE, respectively. Transposition to the reaction OfZ ne = RS(Z-n) involving two species soluble in the electrolyte phase is also immediate. Equations 6 and 7 are directly applicable with the following transformations : z to n; v+ to vo and V M to VR,the positive fluxes being toward the electrode for vo and toward the bulk of the solution for VR. The measured current density is also given by eq 8 with the above change of notations.
+
+
Forms of the General Equations. We consider this case because it has been studied experimentally2~a and because it shows, in a simple manner and for a concrete example, the theoretical impossibility of a priori separation of faradaic and charging currents. We assume the following conditions. (a) The electrode area A varies and the overvoltage q is applied a t time t = 0 a t which A begins to vary. Thus, the electrode is a t the equilibrium potential before A varies. (b) The potentiostat-cell circuit is supposed to have a zero time constant. (c) The low overvoltage approximation is valid. The general eq 6 to 8, which were derived for a constant electrode area and any overvoltage, must now be written for the conditions stated above. Thus
YM
= V+
i
=
+ zF(r+),,o(l/A)(dA/dt)
(11)
[(r+),=o 4- (r~),=oI(l/A)(dA/dt)
(12)
+ + ZFr+),=o(l/A)(dA/dt)
ZFV+ (4
(13)
where eq 12 is not needed here (no amalgam). Note that i for the conditions assumed here also includes an infinite component a t t = 0 which results from charging of the double layer from q = 0 to a finite q in an infinitely short time by means of a supposedly ideal potentiostat. We shall neglect this component of i. The Problem. We shall use the usual low overvoltage approximation for i t , that is i f = i0[1- (c/cs)z=o
+ (zF/RT)q]
A better approximation will not be used since our main purpose is not a detailed description of the iy-t relationship but rather the analysis of the charging process. We also assume (l/A) (dA/dt) to be constant because the mathematics are considerably simplified. [One has (l/A)(dA/dt) = t-' for an ideal expanding dropping mercury electrode. ] Finally, we neglect the movement of the metal-electrolyte boundary resulting from the condition that (l/A)(dA/dt) be constant. Thus, we do not correct Fick's equation in a manner similar to that developed by Ilkovic for the dropping mercury electrode. A treatment for the actual conditions a t a dropping mercury electrode is being developed but is not expected to reveal any new feature about the principles involved. Equation 11is now i0[1-
(c/cs)z=~
+ (zF/RT)q] =
-zFD( b c / b ~=) 0, + ZF(I?+),
Application to a Metal Ion-Pure Metal Electrode of Varying Area at Constant Overvoltage
if = ZFV+
2377
(14)
where io is the exchange current density, c is the concentration of cs is the bulk value of c, 2 is the distance from the electrode, and R and T are as usual.
=0
(l/A) (dA/dt)
(15 )
where D is the diffusion coefficient of M+II. The minus sign in front of the flux term results from the convention on the direction of v+ (see eq 6). Furthermore, onehasc = c s f o r z 2 O a t t = O a n d c + c s f o r z + m fort 3 0. The solution of Fick's equation was obtained by Laplace transform and the following current density i was obtained according to eq 13
i
=
[io(zF/RT)a
exp(X2) erfc(X)
- zF(I'+),=o(l/A)(dA/dt)]
+ (a + zFr+),=o(l/A)(dA/dt)
(16)
where X = i0t1/2/zFD'/2cs
(17)
Note that the current i also includes the infinite component a t t = 0 discussed in connection with eq 13. If io + a (so-called reversible process) eq 16 becomes after expansion of erfc(X) for a large argument
i
= zFcs(D/at)'/2(zF/RT)q
(q
+
+ zFr+),=o(l/A) (dA/dt)
(18)
where the term in t-'/' is the usual expression for the diffusion current density in this particular case.
Discussion Equation 16 will be discussed by comparing it with the expression of i derived by a priori separation of v us. the point of zero charge. The values of the potential $2 in the plane of the closest approach were taken for 0.1 M KCl according to Grahame and Parsons.'a This example corresponds approximately to Zn+*discharge on Zn amalgam in a 0.1 M univalent supporting electrolyte on the assumption that no complex is formed ( z = 2). (13) D.C. Grahame and R. Parsons, J . Am. Chem. Soc., 8 3 , 1291 (1961).
Volume 70, Number 7
Julv 1066
PAULDELAHAY
2378
faradaic and charging processes. One obtains by using the charging current density for an ideal polarized electrode il
=
io(zF/RT)q exp(X2) erfc(x)
201
I
1
I
2
3
I
\ \
\
+
n;=o(l/A)(dA/dt)
I
\
(19)
(See also the remark about eq 13 and the infinite charging current at t = 0.) The faradaic component in eq 19 corresponds to the usual potentiostatic conditions at low 0vervoltage.1~ Conversely, we obtain by assuming charging as an ideal reversible electrode and neglecting the infinite current at t = 0 i2
=
io(zF/RT)qexp(X2)erfc(X)
+
+
(Q zFr+),=o(l/A)(dA/dO (20) The difference between eq 16, 19, and 20 can be quite pronounced as shown in Figure 1. This diagram was prepared for Fr+ = 5 pcoulombs cm-2 and c, = mole ~ m - ~These . data correspond to significant but not particularly strong adsorption. We note from Figure 1that i +i~ for t +0
i +i 2 for t + m There is a progressive transition in charging behavior from the ideal polarized electrode (eq 19) to the reversible electrode (eq 20). This is readily seen by considering the limiting forms of eq 16 for X --+ 0 and X a. The physical interpretation is as follows: at t = 0 there is no time for charge separation or recombination to occur; at t + m the external faradaic current approaches zero and all ions are produced or consumed by charge separation or recombination. We also note that reversible electrode behavior in charging prevails at any t when io + a (see eq 18). As practical limits one can set --+
exp(h2) erfc(X)
> 0.95 for X < 0.05 (charging as ideal polarized electrode)
exp(X2)erfc(X)
< 0.05 for X > 10 (charging as ideal reversible electrode)
If one sets, for instance, z = 1, D = cm2 sec-l, and c, = mole ~ m - one ~ , finds X < 0.05 for iot”’ < 1.5 X amp cm+ set'" and X > 10 for id” > 3 x 10-3 amp cm-2 secl”. If measurements are at the scale of 1 see, a moderately slow process behaves in double-layer charging as an ideal polarized electrode, and a moderately fast process behaves in double-layer charging as an ideal reversible electrode. If the time scale decreases, the corresponding limits of io increase accordingly. The Journal of Physical Chemistry
0
4
x
5
Figure 1. Measured current as a function of t,he parameter X (proportional to tl/’) for the following data: z = 1, D = cm sec-1, cB = 10+ mole cm-8, (l/A)(dA/dt) = 1 sec-1, amp cm+, 9 = 5 mv, T = 25’, FT+ = 5 X io = pcoulomb cm-2. The ri)s are arbitrarily set to zero for all ions except M +’ (the corresponding term is independent of time).
Charging at the Equilibrium Potential.
If one sets
q = 0 in eq 16, one sees that the charging current still
depends on exp(X2) erfc(X), Le., on io. The previous conclusions about the limiting cases for t = 0 and t + a also apply here. The physical interpretation is as follows : when A varies, the consumption or production of M+z causes the concentration of M+.just outside the diffuse double layer to be different from the bulk value c,; since E is maintained potentiostatically a t the equilibrium value corresponding to cs, there is in fact an overvoltage which drives the separation or recombination process. Determination of io, q, and I?+. The procedure for the determination of these quantities will be outlined to show that a posteriori separation of the various parameters is feasible. Thus, a plot of i against t”’ for X > 1, and consequently q is obtained since r+is known from the previous plot. Thus, the transition in charging behavior from an ideal polarized electrode to an ideal reversible electrode allows complete analysis by extrapolation at t = 0 and t + a.
+
(14) H. Gerischer and W. Vielstich, Z. Physik. Chem. (Frankfurt), 3, 16 (1955).
RADIOLYSIS OF 8-METHYLPENTENE-1
Conclusion Faradaic and charging processes cannot be separated a priori in nonsteady-state electrode processes because
of the phenomenon of charge separation or recombination a t the electrode-electrolyte interface without flow of external current. Charging behaviors as ideal polarized or reversible electrode represent only two limiting cases of a more general case. Much of what has been done with relaxation and perturbation methods for fast electrode processes will have to be reexamined and possibly revised in the light of the present ideas. This task has already begun for impedance measurements4 and is being pursued. Some and perhaps most of the
2379
glaring discrepancies on kinetic data obtained by different methods, as reported in the literature, may possibly be removed. (Other possible sources of discrepancies must, of course, be kept in mind.) Interpretation of double-layer phenomena for nonideal polarized conditions should also receive a new impetus from this work.
Acknowledgment. This investigation was supported by the National Science Foundation. The author thanks Drs. de Levie and G. Tessari for discussion of Sluyters' work and Dr. R. Parsons (University of Bristol), who kindly went over the initial draft of this paper.
Observations on Trapped Electrons and Allyl Radicals Formed in 2-Methylpentene-1 by
y
Radiolysis at Low Temperature
by D. R. Smith and J. J. Pieroni Research Chemistry Branch, Atomic Energy of Canada, Limited, Chalk River Nuclear Laboratories, Chalk River, Ontario, Canada (Received February 11, 1966)
The cobalt-60 y radiolysis of 2-methylpentene-1 (2-MP-1) glass a t 77°K has been studied by electron spin resonance (esr) methods. The esr spectra due to trapped electrons and an allyl-type radical are observed. When biphenyl is present, the esr spectrum of the biphenyl anion replaces that of trapped electrons. The results suggest that the allylic radical is formed via isomerization of the parent ion (2-MP-1)+ + (2-MP-2)+. An interesting ultraviolet photoinduced conversion of the allylic radical to a different allylic radical is observed a t 77°K. No free radicals resulting from hydrogen atom addition to olefin are detected.
Introduction This work is part of a series of investigations'-* in which electrons and free radicals, trapped in organic glasses during y radiolysis at low temperature, are studied by electron spin resonance (esr) spectroscopy. Our previous measurements, on trapped electrons and radicals or radical ions in irradiated 2-methyltetrahydrofuran (MTHF), demonstrated that esr data not only provide a check on data obtained by optical ab-
sorption spectrophotometry4 but also yield additional information. Hence, it was decided to study the radiolysis of an olefinic compound in which trapped electrons have been observed. ~
(1) D. R. Smith and J. J. Pieroni, Can. J . Chem., 42, 2209 (1964). (2) D. R. Smith and J. J. Pieroni, ibid., 43, 876 (1965).
(3) D. R. Smith and J. J. Pieroni, ibid., 43, 2141 (1965). (4) M. R. Ronayne, J. P. Guarino, and W. H. Hamill, J . Am. Chem. Soc., 84, 4230 (1962).
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J u l y 1966
