J. Electroanal. Chem., 66 (1975) 235--247
235
© Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands
Preliminary note
RESONANCE RAMAN SPECTROELECTROCHEMISTRY
V. INTENSITY TRANSIENTS ON THE MILLISECOND TIME SCALE
FOLLOWING DOUBLE POTENTIAL STEP INITIATION OF A D I F F U S I O N
C O N T R O L L E D ELEC~rRODE REACTION
DAVID L. JEANMAIRE* and RICHARD P. VAN DUYNE**
Department of Chemistry, Northwestern University, Evanston, Ill. 60201 (U.S.A.)
(Received 4th October 1975)
The raison d'etre of spectroelectrochemistry is to provide superior molecular
specificity with respect to the usual electrochemical observables (e.g., current,
charge, potential, time etc.} for purposes of: (1) identification and/or detection; (2) structural characterization; and (3) kinetic monitoring of electrogenerated species formed either on the electrode surface, in the electrochemical diffusion layer adjacent to the electrode surface, or in the bulk of solution.
Restricting the present discussion to the subset of species electrogenerated in
solution, one can distinguish a wide variety of product types which can be
formed from a neutral starting material, R. These include a chemically
distinguishable neutral, N; radical ions, R ~ or R'+; a neutral free radical, R ' ; a
carbanion, R - , or carbonium ion, R÷; the diions, R 2- or R:+; as well as various
dimeric products R2, R ~ ' , . . . etc. The spectroscopic techniques which to date
have been used to carry o u t spectroelectrochemical studies on such species include electronic absorption spectroscopy (UV-VIS-NIR) [1, 2], electron spin
resonance (ESR) spectroscopy [3], infrared (IR) spectroscopy [4, 5], normal
spontaneous Raman spectroscopy (NRS) [6, 7], resonance Raman (RR) scattering spectroscopy [8--10], resonance Raman excitation spectroscopy [11l,
nuclear magnetic resonance (NMR) spectroscopy [ 12, 13], and mass spectrometry (MS) [14, 15].
By far, the greatest impact on electrochemistry to date has been made by
electronic absorption spectroelectrochemistry. This is due primarily to the fact
that this technique: (1) can be used to study any of the electrogenerated
species mentioned above requiring only that they absorb light somewhere in
the UV-VIS-NIR range which is a virtual certainty; (2} can be adapted to a
wide variety of experimental situations -- surface studies, aqueous as well as
* 1975 ACS Analytical Chemistry Division Fellow.
**Alfred P. Sloan Foundation Fellow 1974--1976. To whom correspondence should be
addressed.
236
non-aqueous solutions, transmission, specular reflection, and internal reflection arrangements, thin-layer electrochemistry, hydrodynamic electrodes, etc.;
and (3) has a wide dynamic range of time scales for kinetic observations -hours to microseconds. The main limitation of electronic absorption spectroscopy as a spectroelectrochemical monitor is that in condensed media {i.e.,
solution) the absorption spectra are very broad and not particularly well resolved due to extensive overlapping of excited state vibrational levels and
strong interactions with the medium. Consequently this technique does not, in
general, provide sufficient molecular specificity to permit unambiguous a priori
product identification (especially for isotopically labeled species). In addition
for kinetic studies one is frequently faced with the problem of overlapping absorption bands at the monitoring wavelength [ 16|. This problem can range
from a minor annoyance to total intractability depending on the complexity
of the electrode mechanism being examined. Thus the primary motivation for
the development of the other spectroelectrochemical tools cited above stems
from the need to overcome the low resolution-overlapping band limitation of
the electronic absorption spectroscopy approach. The successful interfacing of
ESR, IR, NRS, NMR, and MS with electrochemistry has been achieved but unfortunately at the expense of either (or b o t h ) ( 1 ) drastically restricted range of
applicability or (2) low sensitivity leading to loss of kinetic monitoring ability
and compression of the accessible time scale.
In our opinion resonance Raman spectroelectrochemistry (RRSE) is the approach which shows the greatest promise of any technique now known for
combining the high resolution molecular specificity characteristic of ESR, IR,
NRS, NMR, and MS with the broad applicability to various types of species
and experimental arrangements as well as the time scale flexibility for kinetic
studies characteristic of electronic absorption spectroelectrochemistry. To date
we have demonstrated that RRSE can provide high resolution "line" spectra
with excellent S/N of the electronic ground state of cyanocarbon anion
radicals in nonaqueous solution using bulk concentrations of the starting
material that are well within the normal range of electrochemical studies (i.e.,
10 -~ M--3 x 10 -3 M) [8, 9]. RR spectra can be obtained in either of two
electrogeneration modes: (1) controlled potential coulometric electrolysis in
bulk solution or (2) cyclic potential step electrolysis under semiinfinite mass
transport conditions. In other studies we have demonstrated the potential of
RRSE for "fingerprint" electrolytic product identification w i t h o u t the necessity for sample work-up [10]. This capability should be broadly useful in
organic, inorganic, and organometallic electrosynthetic investigations. It should
also be noted that through the use of RR excitation spectroscopy (viz., the
measurement of the intensity of a single R R line as a function of laser excitation frequency, P0) direct information a b o u t the excited electronic states of
electrogenerated radical ions can be obtained [ 11 ].
This communication describes the extension of the resonance Raman
intensity (RRI) vs. time transient monitoring capabilities of RRSE from the
time domain of a few seconds [8] into the tens of milliseconds regime. This
237
accomplishment was facilitated by an improved R R S E spectrometer employing an Ar + laser pumped, CW tunable dye laser as the excitation source and a
multichannel analyzer based signal detection system. The CW dye laser was
used to maximize the R R signal intensity by exciting the species of interest at
its electronic absorption maximum and the multichannel analyzer was used to
signal average the digital (photoelectron counts) transients in order to improve
the overall S/N. Signal averaging of analog transients has been previously employed by Kuwana in both transmission [17] and internal reflection [18, 19]
VIS absorption spectroelectrochemical studies for S/N enhancement. For
simplicity in this paper we have restricted ourselves to the discussion of R R I
vs. time transients following double potential step initiation of a diffusion
controlled electrode reaction with no complications due to follow-up chemical reactions. The model system chosen for the simple E mechanism:
A± ne-
.~ B
was the one-electron oxidation of N,N,N',N'-tetramethyl-p-phenylenediamine
(TMPD) to form its cation radical (Wurster's blue, TMPD'+):
TMPD ~ TMPD "+ + e -
E ° ~ E,/~,~ = +0.11 V vs. SCE
(2)
In addition to its electrochemical simplicity [20, 21], the TMPD/TMPD "+
system was subjected to RRSE examination because TMPD is an extremely
strong electron transfer d o n o r and we have a long range interest in trying to
understand the detailed vibrational relaxation dynamics of homogeneous
electron transfer reactions [22, 23]. The vibrational frequency shifts obtained
by comparing the R R scattering spectrum of TMPD "+with the NR scattering
spectrum (or if experimentally accessable the UV-RR scattering spectrum) of
TMPD will facilitate such investigations.
Experimental
The TMPD used in this work was prepared and purified as described by
Bard et al. [ 24]. The acetonitrile and tetrabutylammonium perchlorate (TBAP)
used as solvent and supporting electrolyte respectively were procured and
purified as described previously [8 |. All solutions were degassed with highpurity nitrogen in accord with standard electrochemical practice.
The electrochemical apparatus including potentiostat, signal generators, and
associated signal monitoring devices for cyclic voltammetry and double
potential step measurements has been described elsewhere [ 8].
All RRSE experiments to be discussed in this paper were carried o u t under
conditions where semiinfinite diffusion mass transport conditions prevail. The
RRSE cell has been previously described and is pictured in Fig.lB of ref.8
along with the associated optics for shaping the laser beam, directing it toward
the electrode surface, and collecting the Raman scattered light and focusing it
on to the entrance slit of the monochromator. In order to avoid "edge effects"
and to illuminate efficiently the rectangular shaped, bulk platinum working
238
electrode, the laser beam used to excite the electrogenerated species (circular
cross section, ca. 1 mm diam.) is first passed through a cylindrical lens so that
it is condensed into a nearly rectangular cross section of area, A ', which is less
than the geometric area, A, of the working electrode. The total scattering
volume is, therefore, defined by the rectangular cross section of the condensed
laser beam (ca. 3.0 mm x 0.5 mm) and the distance between the planar
electrode surface and the rear surface of the electrochemical cell front window
(ca. 3.0 mm). The scattering volume, of course, completely includes the
electrochemical diffusion layer where the resonance Raman active species is
formed.
The m o n o c h r o m a t o r used to resolve spectrally the Raman scattered light in
these experiments is a 0.75 meter Spex Model 1400-II double m o n o c h r o m a t o r
equipped with a cooled (-20°C) RCA C31034 photomultiplier tube and
standard Ortec, low level threshold, p h o t o n counting electronics. The Ar ÷ and
"jet-stream" CW dye lasers used in this work have been described previously
[9, 11]. The use of a pre-monochromator to remove the superradiant fluorescence emission from the dye laser o u t p u t beam w3s found to be absolutely
necessary in experiments where the laser beam is backscattered off a reflective
electrode surface. If a pre-monochromator is not used, the broad band
Rayleigh light collected by the fore-optics and m o n o c h r o m a t o r swamps out
the comparatively weak resonance Raman signals. An analogous problem occurs with plasma line emission from an Ar ÷ laser so that interference filters or
the pre-monochromator must always be used in "off-the-electrode" scattering
experiments.
RR scattering spectra of species generated in the electrochemical diffusion
layer were obtained by scanning the double m o n o c h r o m a t o r normally from ca.
100 cm -~ to 3000 cm -~ while driving the potentiostat with the cyclic square
wave potential program shown in Fig.lA. This waveform sets up a steady state
concentration profile of the resonance Raman active species in the diffusion
layer a few pm in front of the electrode surface. Raman spectra were processed as described in previous publications [8]. Laser power measurements
were made with a Coherent Radiation Model 210 broad band power meter.
The Raman frequencies reported here are accurate to +2 cm-~. The Raman
spectrometer was wavelength calibrated using Ne lamp emission lines.
In order to obtain RRI vs. time transients of individual Raman spectral
bands with high S/N and double potential step switching times, T, less than ca.
250 ms, it was necessary to signal average individual transients. For this purpose the "Nim Slow" o u t p u t signal of the Ortec discriminator was fed into
the multichannel scaling input of a Nuclear Data Model 2400 Multichannel
Analyzer (MCA). The MCA was in turn pre-triggered by a synchronizing signal
which preceded the leading edge of the double potential step, signal averaging
waveform (Fig.lB) used to drive the potentiostat. The voltage limits on these
potential step waveforms should be set at least 60In mV past the corresponding peak potential, Ep, in the cyclic voltammogram of the system under investigation in order to drive the surface concentrations of the appropriate
species to zero.
239
Fq
i
Li
TIME
t "r"~ ....
"y"....
TIIVE
>
Fig.1. Applied potential waveforms used for obtaining: (A) RR scattering spectra of electrogenerated species in the diffusion layer and (B) signal averaged, double potential step RRI
vs. time transients of the individual vibrational features in a RR scattering spectrum. Waveform frequencies, pulse switching times, r, and duty cycles, r ' / r , a r e given in the text.
Electronic absorption spectra were taken on a Cary Model 14 spectrophotometer.
Results and discussion
The presentation and discussion of RRI vs. time results requires a very brief
review o f TMPD electrochemistry and some preliminary discussion of the
electronic absorption spectrum and RR scattering spectrum of TMPD +".
The cyclic v o l t a m m e t r y of TMPD in acetonitrile is shown in Fig.2. Scanning
in the anodic direction, peaks due to formation of TMPD "+(peak A, Epa =
+0.138 V vs. SCE) and TMPD 2÷ {peak B, Epa = +0.715 V vs. SCE) are observed.
These results are in excellent agreement with those of Kissinger [21]. The first
wave fits the criteria for both chemical and electrochemical reversibility on
this time scale [25]. T he second wave is less ideal since it is influenced by the
h o m o g e n e o u s electron transfer reaction:
TMPD 2+ + TMPD ° ~- 2 TMPD "+
(3)
Controlled potential reversal c o u l o m e t r y in bulk solution shows t h a t TMPD "+
is generated quantitatively and is chemically stable for periods of m a n y hours
[26].
The electronic absorption spectrum of electrogenerated TMPD t is shown in
Fig.3. TMPD ° absorbs light only in the UV (less than 3700 £) [27]. Also
shown in Fig.3 is the fact that an Ar ÷ laser pum ped, rhodam i ne 6G (R6G) CW
dye laser can be used to excite TMPD "+at its lowest energy absorption
240
TMPD
/
~
T
,:
B
I
+0.8
--
__.L--_
+0.4
~O~.G -
I
+0.2
I,-0.0
E/voli's(vs.SCE 1
~
Fig.2. F i r s t - s c a n c y c l i c v o l t a m m o g r a m o f 1 . 0 0 m M T M P D in a c e t o n i t r i l e c o n t a i n i n g 0 . 1 0 M
T B A P at a p l a t i n u m disk m i c r o e l e c t r o d e . T h e s c a n rate = 0 . 2 0 0 V s -~ .
3272C
. . . .
H C/ ~
RGG
"
\C~4
IG
co
oJ
~T~
X
i
4
0
.
,,
300
,
400
,.
,.._
500
,
.
, ,..
GO0
I
WAVELENGTH/rim
+
.
.
.
Fig.3. Electronic absorption spectrum of TMPD" from 210 nm to 650 nm m acetomtrde
c o n t a i n i n g 0 . 1 0 M T B A P . T h e T M P D "~ w a s f o r m e d b y c o n t r o l l e d p o t e n t i a l e l e c t r o l y s i s in
b u l k s o l u t i o n at + 0 . 2 0 V vs. S C E .
maximum (612 nm.). This absorption maximum represents the 0-*0 vibronic
transition of the : B3g-.2 B2u°) electronic transition (Y axis polarized) [ 28, 29].
The symmetry designations of the 2TMPDt (D2h) ground and lowest
electronically excited state are based on a coordinate system with the Y
cartesian axis parallel to the long C2 molecular axis and the X cartesian axis
parallel to the short C2 molecular axis.
The RR scattering spectrum of TMPD "+in the diffusion layer of a platinum
241
electrode formed under cyclic potential step (CPS) conditions at 10 Hz repetition rate and excited with the R6G dye laser tuned to 6120 A is presented in
Fig.4. Since no additional bands were observed beyond 1628 cm -~ , only the
100 cm-' to 1900 cm -~ range is shown in the figure. The two Raman bands at
379 cm-' and 918 cm-' which are marked with an S are CH3CN normal
Raman bands and the sharp shoulder at 931 cm -~ is the normal Raman, totally
symmetric C1--O stretch of ClO4- contributed by the supporting electrolyte.
The remaining 8 lines at 328 c m - ' , 514 c m - ' , 1171 c m - ' , 1226 c m - ' ,
1375 c m - ' , 1419 c m - ' , 1509 cm-' and 1628 cm-' are all TMPD "+vibrational
modes. The depolarization ratios were measured for some of the strong and
medium intensity Raman bands in this spectrum and were found to be 1/3.
This is indicative of the fact t h a t only one diagonal element of the Raman scattering tensor is resonance enhanced [30]. Thus the TMPD "+bands in Fig.4 can
be assigned to totally symmetric vibrations as is the usual circumstance in
resonance Raman spectroscopy [30] where the scattering mechanism does not
involve configuration interaction between doubly degenerate excited electronic
states or vibronic coupling between states of different electronic symmetry.
The 8 Raman lines of TMPD "+that are observed do not appear to be overtones
or combination bands so they must be assigned to totally symmetric fundamentals. A possible exception to this is the 1509 cm-' band which may have a
1499 cm -~ (328 cm-' + 1171 cm-' ) shoulder on its anti-stokes side. The lack
of overtones or combinations is unusual considering that rigorous resonance
Raman excitation [30] is involved here and there is clear vibrational fine structure developed in the : B3g-~: B2u(') transition. A more detailed interpretation of
~3(-~ ~ -
42
CH
CPS TOHz
zN
rl
ii
s
~ o~
-
=, -
,
OR
S
:&
co
I
!GO0
12%/C M_I 800
I
,400
Fig.4. R e s o n a n c e R a m a n s c a t t e r i n g s p e c t r u m o f e l e c t r o g e n e r a t e d T M P D "+, [ T M P D ] =
3.0 raM; laser p o w e r = 35 roW; b a n d p a s s = ca. 2 cm-".TMPD "+was e l e c t r o g e n e r a t e d b y cyclic
p o t e n t i a l step electrolysis a t 10 Hz (see w a v e f o r m in F i g . l A ) in 0.10 M T B A P / C H ~ C N . T h e
s p e c t r a l scan r a t e was 0 . 3 3 3 3 A s -I using a 1.00 s counting gate interval. S u p e r r a d i a n t d y e
laser f l u o r e s c e n c e was r e m o v e d w i t h a q u a r t z p r i s m ( L i t t r o w m o u n t e d ) p r e - m o n o c h r o m a t o r .
242
the RR scattering spectrum of TMPD "+will be reserved for a forthcoming paper
in which its spectrum will be discussed in relation to the RR and NR spectra of
related molecules such as TMPD °, TMPD-d~
° ~ TMPD-d4
"+,p-phenylenediamine
444neutral (PPD ° ), PPD-d4 °, PPD-d8 °, PPD', PPD-d,', and PPD-ds" [31]. For purposes of the present discussion on RRI transients, however, we can unambiguously identify the intense 1628 cm -~ feature as the totally symmetric
C--C ring stretching mode by analogy with other D2h benzenoid radical ions
and their corresponding neutrals [9, 31]. The remaining results will focus on
the RRI vs. time transients of the 1628 cm -~ band under double potential step
conditions.
The signal averaged (1000 repetitions) double potential step RRI vs. time
behavior of the 1628 cm -~ C=C (Ag) ring stretching mode of TMPD "+excited
with the R6G dye laser at 6120 A is pictured in Fig.5. With T = 0.050 s and a
d u t y cycle, r'/T, of 19, the total data collection time to obtain this profile was
16.67 min. Unlike the earlier RRI--t results on TCNE= [8], the S/N of the
present data is sufficiently good that one can reasonably consider a quantitative analysis of its time dependence. The form of the RRI--t profile is, as
expected, reminiscent of the c h a r g e - t i m e behavior of double potential step
chronocoulometry [32] and the absorbance--time behavior of chronoabsorptometry [ 1 ].
In addition to the usual diffusion problem for the E mechanism with initial
and boundary conditions appropriate to the double potential step, a mathematical analysis of the RRI--time experiment involves consideration of the following effects which are peculiar to RRSE:
%
d
t"
o0
CM
~D
N}--
/
I
Z
W
._
1
0
I
50
I(~0
TIME/ms
150
260
Fig.5. Signal averaged d o u b l e p o t e n t i a l step R R I vs. time profile for the 1628 c m -~ TMPD +
b a n d during the o n e - e l e c t r o n o x i d a t i o n o f TMPD. 1000 averages; 3.0 ~
TMPD in 0.1 M
TBAP/CH~CN; R 6 G d y e laser p o w e r at the f r o n t surface o f the R R S E cell w i n d o w = 35 mW
at 6120 A; s p e c t r o m e t e r b a n d p a s s = 2.0 c m - ' ; p o t e n t i a l step limits = +0.31 V vs. SCE and
- 0 . 0 9 V vs. SCE; r = 0.050 s; r ' / r = 19; b a c k g r o u n d has b e e n s u b t r a c t e d o u t ; 256 data points.
243
(1) Time and distance dependent heating of the electrochemical diffusion
layer resulting in mixed convective-diffusive mass transport which is caused by
radiationless dissipation of the laser excitation energy in any species that absorbs at v0.
(2) Time and distance dependent re-absorption of R R scattered photons by
any (or all) of the species involved in the electrode reaction mechanism.
(3) The specular reflection nature of the RRSE laser excitation geometry.
(4) The collection efficiency of the fore-optics as a function of depth of
focus into the solution [33].
(5) Background fluorescence.
A general theoretical analysis of RRI--t experiments will be presented elsewhere [34]. However, the results of that analysis indicate that, if the RRI--t
data are acquired at relatively short r and large r'/r, with low laser power, and
laser excitation at the lowest energy absorption maximum of a particular
electronic transition in the electroactive R R active scatterer, a greatly
simplified theoretical treatment is valid. The data in Fig.5 were intentionally
acquired under such conditions. Thus only the simplified theoretical analysis
will be discussed here. The specific assumptions of that analysis are:
(1) Laser heating is sufficiently small that the concentration profiles resulting from the solution of the appropriate Fick's law boundary value problem
are valid.
(2) Re-absorption of R R photons scattered at a frequency VRR = v0 - AVRR,
where AVRR is the Raman shift (in cm -~ ) of the vibrational mode being
monitored, is negligible so that the overall intensity of the scattered radiation
is directly proportional to the distance integrated concentration profile of the
R R active electrogenerated species, i.
Iij~R(URR,t) ~ of ~° Ci,RR(X,t)dx
(4)
(3) The specular reflection of the laser beam striking the bulk platinum,
planar working electrode at an angle of incidence, ~, is 100% efficient resulting
in a simple correction to the RR intensity of 2/cos ~ [21].
(4) The RR collection efficiency of the fore-optics is not a strong function
of distance over the region of the diffusion layer.
(5) Only the electrode product (species B in eqn.1) is R R active (i.e., absorbs) at v0.
(6) The background fluorescence signal is either absent (an unlikely situation except in aqueous media) or is not electrochemical modulated to a significant extent.
In non-specular reflection situations where the concentration of the R R scatterer is uniformly distributed with respect to distance and is n o t time dependent, the intensity of R R scattered radiation from species i at VRR is given by
[35]:
/i,RR(VRR) = ( 27ns / 32c4 ) [~p,o I~p,a 12]i,RRS(~R)V4RRIo (v0)Ci.RR
(5)
where %,o is an element of the Raman scattering tensor, p and a are cartesian
244
coordinates (x, y, or z), 10(v0) is the intensity of the laser beam incident on
the sample, S(~RR) is a wavelength dependent sensitivity factor for the
spectrometer/detector system, and ci,RR is the molar concentration of the RR
scatterer. For our purposes eqn.(5) can be simply rewritten as:
Ii,RR (uaR) = Ji,aR (VRR)I0 (u0)Ci,RR
(6)
where Ji,RR (~RR) is the molar scattering coefficient for species i. In the present
specular reflection, electrochemical situation, however, the concentration of
the R R scatterer is, of course, both distance and time dependent so that
eqn.(6) must be modified as follows:
Ii~RR(t~RR, t) = (2/cos ~) Ji,RR (gRa)Io
(Vo)
of
~
Ci,RR(x, t) dx
(7)
The double potential step concentration profile for species B (TMPD "+) in
eqn.(1) is well known [1] and is given in the Laplace plane by:
CB,RR (x,s) = CBJ~R (0,s) exp [ - ( s / D B )'/2x ]
(8)
where for:
t ~< T: CB(0,s) = (C°A/S)(DA/DB) 1/2
(9a)
t > T: CB(0,s)-- (C°A/S)(DA/DB)I/2[1 - e x p ( - s T ) ]
(9b)
Combining eqns.(7), (8) and (9), performing the indicated integration, and inverse transforming back to the time plane gives:
IBj~R (~RR, t ~ r) = (4/COS i3)JB~RR(VRR)I0 (Vo)C°A(DAt/Tr) 1/2
IBJ~R(VRR,t > r) = ( 4 / c o s ~ ) J B ~ t R ( V R R ) I o ( v o ) c ° A ( D A / n ) l / 2 [ t
(10a)
~/2 - (t - T)I/2I (10b)
As is the usual custom in the treatment of double potential step response data
[32], the RRI ratio for B can be formulated to yield:
RB,RR(VRR j ) = I (IB,RR(r) - I B , R R ( 2 r } ) / I B , R R ( T } I= 2 - 21/2 = 0.5858
(11)
In non-kinetic systems such as the E mechanism, deviations from the theoretical value of 0.5858 can be used to diagnose breakdowns in the assumptions of
this analysis.
Figure 6A shows the RRI--t data for the forward step of Fig.5 plotted vs.
t 1/2 and Figure 6B shows the corresponding reverse step data plotted vs. 01/2=
t ~ - ( t - r) 1~. The excellent linearity and zero intercepts of these plots indicate
at least that the assumptions of negligible diffusion layer heating, re-absorption, etc. are sufficiently valid to account quantitatively for the time dependence of the 1628 cm-' TMPD "+RRI--t profile. Also we note that the value of
the R R I response ratio at r = 0.050 s is 0.576 which is in excellent agreement
with theoretical expectation. We have done some preliminary experiments to
investigate breakdown of the theoretical assumptmns. For the TMFD ° system
excited at 6120 £, we found that if r is of the order of 1.0 s.significant selfabsorption of R R photons and diffusion layer heating occurs leading to distortion of the t 1~ and 01/~time dependences. Furthermore as the d u t y cycle of the
245
•
A
~D
/
~
~x----~--
4-
--÷
--
_
I
_J
B
25K
"~,
oo~
o,o
~5 -
tl/2 or-
o~-
-
-
0/sl/2
Fig.6. R R I ( 1 6 2 8 cm -t) vs.: (A) t ~ for t h e f o r w a r d s t e p and (B) 0 ~ = t ~' - (t - r) ~ for t h e
reverse s t e p o f the o n e - e l e c t r o n p e r f e c t l y reversible o x i d a t i o n o f TMPD. T = 0 . 0 5 0 s;
i n t e n s i t y values t a k e n f r o m Fig.5.
,
,'o
'
2'o
'
~'o
'
~'o
Fig•7. R R I r e s p o n s e ratio, RB~tR (VRR ,r = 0.050 s), as a f u n c t i o n o f t h e d u t y cycle, r'/r, o f
the signal averaging, d o u b l e . p o t e n t i a l s t e p waveform• T h e o r e t i c a l value o f RB,RR (pRR ,r) =
2 - 2 ~ = 0.5858•
246
signal averaging double potential step waveform is reduced below r'/r = 9, the
RRI response ratio, RB~RR(VRR,r = 0 . 0 5 0 s), increases to values significantly
greater than the value of 0.5858 predicted for single-shot double potential step
excitation. These results are presented in Fig.7 and define the minimum value
of the signal averaging waveform d u t y cycle that will give data that can be
evaluated in terms of single-shot theory. This situation exists because for
r'/r < 9 the initial conditions are not reestablished during the pulse " o f f " time.
Acknowledgement
The support of this research by the National Science Foundation
(MPS74-12573 A01) is gratefully acknowledged. One of us (D.L.J.) also
acknowledges a fellowship from the ACS Analytical Chemistry Division
sponsored by the Perkin-Elmer Corporation for the academic year 1975--1976.
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and references therein.
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