J. Php. Chem. 1003, 87, 2485-2492
2485
Optical Detection Electric Field Jump Study of Dye Dimerization in Glacial Acetic Acid Robert J. Rhlnesmith and Paul Hemmes' ChemLstry Department, Rutgers Unlverslty, Newark, New Jersey 07102 (Received: September 22, 1982; I n Final Form: January 6, 1983)
An optical detection electric field jump (&jump) instrument was built by using either a xenon arc lamp or an argon ion laser source. The chemical system studied was the dimerization of methyl yellow (MeY). Its relaxation times in the concentration range 6.3-250 jtM in acetic acid were best fit by a mechanism involving triple and quadrupole aggregations of the dye molecule. The forward and reverse rate constants for triple-ion formation were found to be k f = 12.8 X 1O'O (M s)-', K, = 2.8 X lo5 s-', while the equilibrium constants for triple and quadrupole formation were KT = 138 M-' and KQ = 32 M-l. In the course of this study a light-induced relaxation process was observed which may be a photochemically induced cis-trans isomerization of the dye. In addition, an analysis of the factors which contribute to optimizing the signal-to-noise ( S I N ) ratio of the E-jump experiment has been carried out. It was found that an optimum concentration exists for the experiment, and the observed effect will have significant amplitude only in a limited region about this optimum.
Introduction The electric field jump instrument, first used by Eigen and De Maeyer' to study fast protonation reactions, remains one of the least commonly used relaxation methods. This technique employs a high electric field to shift the equilibrium of a system, and either this shift or the return to equilibrium is then monitored to measure the rate of reaction. Reactions which involve the formation of ions are the most often studied. The field dependence was first observed by Wien in 19282 and was theoretically studied by Onsager in 1934.3 According to Onsager K(E)/K(O) r 1 + b (1) K ( E ) is the dissociation constant at field strength E , K(0) is the value at zero field, with b = 9.636E/DP where E is in V cm-l, and D is the dielectric constant. Equation 1 is valid only for small values of b. While this theory has been extended and improved by McIlroy and Hill: the approximation given by eq 1 remains valid. Accordingly, one would expect, that the relative change in the dissociation constant would increase with decreasing dielectric constant. I t was therefore expected that in nonaqueous, low-dielectric media the detection of the Wien effect would be more readily observable than in water. Strengthening this assumption was the fact that the lower electrical conductances of the solutions would permit larger field strengths for longer pulse durations. Some of these expectations were not fully borne out in practice and it proved to be difficult to find systems which exhibited an optically detectable Wien effect in nonaqueous media. We therefore began a study to find out why the qualitative predictions failed so often. Other studies in our laboratory had been directed toward investigation of weak electrolytes in low-dielectric media. Kinetic studies of these processes were rather rare but theoretically and experimentally it had been found that very concentration-dependent relaxation times might be expected in such systems. One place where aggregation had been well documented was in the formation of hydrogen-bonded dimers of weak acids in low-dielectric media. A large number of these systems had been studied spectrophotometrically and it was felt that these dyes
* Address correspondence to this author at the Ames Division, Miles Laboratories, Inc., Elkhart, IN 46515.
might make good candidates for an optical E-jump study. Most of these systems proved unsuitable, however, until an analysis of the amplitudes of electric field jump effects was completed. Following this analysis we predicted that the system methyl yellow (p-(dimethy1amino)azobenzene) in glacial acetic acid would be suitable based on thermodynamic data given by K ~ l t h o f f . This ~ proved to be the case. The results of these experiments are the subject of this paper.
Theory Consider a weak acid dissociation HA = H+ + AFor optical detection of the electric field jump experiment, assuming Beer's law holds we have generally, at wavelength h I ( h ) = Io exP(-(t~,~l[A] + +IA,A~[HAI)) (2)
Here I is the light intensity at the detector, the t's are the absorption coefficients associated with each species, 1 = path length, and Io is the incident light intensity (into the cell). In practice we choose a wavelength such that one t is small; for example, if
>> ~ H A , A
~A,X
then eq 2 may be varied with respect to [A-1, resulting in
6 I / I = -t~,~lb[A-]
(3)
Since K = [A-][H+]/[HA], a variation in K leads to
&41 = (6K/K)(2CO)b(l - d / ( l + 41
(4)
with a the degree of dissociation. The term in curly braces in eq 4 has a maximum value of about 0.172 at a = 2lI2 - 1. Co is the total dye concentration. If this equation is substituted into eq 3, we find )(! Eigen, M.; De Maeyer, L. In "Techniqueof Organic Chemistry"; Weissberger, A., Ed.: Interscience: New York, 1963; Vol. 8, part 2. (2) Wien, M. Phys. 2.1928,29, 751. (3) Onsager, L.J . Chem. Phys. 1934,2, 599. (4)McIlroy, D. K.; Hill,J. M. J. Chem. Soc., Faraday Trans. 2 1977, 73,1116. (5) Bruckenstein, S.;Kolthoff, I. M. J.Am. Chem. SOC.1956, 78,lO.
0 1983 American Chemical Society
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The Journal of Physical Chemist@', Vol, 87, No. 14, 1983
But attempts to maximize the relative change in intensity now lead to the conclusion that Coshould be maximized (neglecting the change in a as Co varies). As a predictor of spectrophotometric sensitivity eq 5 is therefore unacceptable. For example, a concentrated dye solution would give rise to virtually complete absorption, so that, even if a relatively large intensity change occurred at the photomultiplier tube (PMT), the resulting signal might remain undetectable in the noise. At first sight we might suspect that only unrealistically high dye concentrations would lead to limiting absorption values, given the great sensitivity of commercial PMT's. The Centronix Q4232B in its normal operating mode (11 stages, 950 V) requires only 6 X lo4 W light flux at the photocathode (at 500 nm) to produce saturation, and the suggested operating point is 2 orders of magnitude below this. At the same time, the equivalent noise input (ENI, the light flux required to produce a signal equal to the W.6 noise in a 1-Hz bandwidth) is only 0.5 X An immediate observation is that the EN1 just cited is proportional to the bandwidth of the detector system. This in turn should be at least equal to, and preferably greater than, the inverse of the shortest relaxation time that we expect to observe. The oscilloscope has a bandwidth limited by the vertical input amplifier to about lo8 Hz, and this would allow relaxation times down to loe7s and below. The EN1 at the operating bandwidth, then, is about 5 X 10-9 w. At the same time, the monochromatic light passing through the E-jump cell can be surprisingly low, especially when narrow monochromator slits and low transfer efficiency optics are employed. Direct readings with a Spectra Physics power meter indicated levels below 0.01 mW (and possibly much less) impinging on the PMT. When low light levels are coupled with dye systems having large extinction coefficients (104-106 M-' cm-'), even moderate solute concentrations may result in inadmissablylow power levels. With all this in mind, it develops that the appropriate quantity to investigate is not 6111 (eq 5), but rather the signal-to-noise ratio ( S I N ) at the detector. Then the change in this quantity caused by a shift in chemical equilibrium can be examined. Specifically, we are concerned with how the chemically induced change in detected light intensity, 6S, compares with the noise level. This quantity is proportional to7 6s N AuR$I (6) where A = the gain of the PMT, ui = the cathode sensitivity (AW-' at specified wavelength), = the quantum efficiency at wavelength A, 61 = the change in light intensity given in eq 3, while the noise level can be written' N A[U~@~I(AV)]'/~ (7) where Au = detector bandwidth (hertz). If the last two equations are combined with eq 3 6S/N [u,&,/Av~]'/~6 1 [u~&,/Av]'/~ cAU'/~6[A]
-
-
-
(8)
Equation 8 permits two immediate observations: first, 6SIN increases with increasing light intensity, as expected, (6) Centronix Instrument Catalog for the Q4232B photomultiplier tube, Seddle Brook, NJ. (7) Ruppel, H.; Witt, H. T."Mothxb in Eneymology";Kurtin, K., Ed.; Academic Preas: New York, 1969; Vol. 16. Schwartz, M. "Information, Modulation, and Noise"; McGraw-Hill, New York, 1959.
Rhinesmith and Hemmes
but also the gain factor (A in eq 6 and 7) has cancelled out. Hence, by reducing PMT gain we can accomodate higher light intensities with no sacrifice in SIN. Generally speaking, the noise attendant with the detection of smaller PMT currents will be more than compensated by the ability to increase I without saturating the PMT. The intensity at the detector must be written in terms of the incident light I,:
6S/N
-
[UA@&/AV]'/~&[A] exp(-d[HA])
(9)
In eq 9, [HA] is presumed to be the absorbing species (note that 6[HA] = -6[A]), and subscripts on the various wavelength-dependent quantities have been dropped). We can now vary 6SIN with respect to any of the parameters shown explicitly in eq 9, or with respect to dye concentration Co, or by some other system variable such as pH. With the notation
K = [H+][A-]/[HA]
(10)
with Co = total molar dye concentration, C, = strong acid concentration, and with the assumption that, for purposes of this analysis, activity coefficients may be ignored, an expression for 6SIN can be written which reflects the parameters K, Co, and C,. (C, is included because many literature studies with aqueous samples acidify the solution to bring the pH close to the pK, of the indicator dye; entirely analogous calculations could be performed for the addition of strong base.) By employing mass and charge conservation, and assuming negligible hydroxide ion concentration, one may write the species given in eq 10
[HA] = Co - [A-] [H+] = C,
+ [A-]
(11)
Equations 11can be substituted into eq 9 as they stand; however, some simplification of notation is desirable, preferrably without losing track of the experimentally adjustable parameters Co and C,. Accordingly, we introduce the dimensionless, reduced parameters x = 2C,/K y 3 C,/K + 1 In practice both x and y have a convenient magnitude (close to unity), and x reflects dye concentration while y is linear in C,. In this notation [A-]/K = [(y2 [HA]/K =
+ 2x)'I2 - y]/'
(12a)
+ y - (y2 + 2x)'I2]/2
(12b) We also need an expression for 6[A-] in eq 9. Equation 4 can no longer be used as it stands because there it is assumed [A-] = [H+]. A straightforward approach is to vary [A-] in eq 12a. There results x + y - (y2 + 2 x ) l / 2 6[A-] = 6K (13) 2y2 + 2x [X
Equations 13 and 12 can now be substituted into eq 9 to yield 6S/N
-
The Journal of Physlcal Chemistry, Vol. 87, No. 14, 1983 2487
Dye Dimerization In Glacial Acetic Acld S/N
TABLE I: Summary of SIN Concentration Dependence dissociation reaction constant
( a r b . units)
+ H’ + AHS + B + S- +
K = [H+][A-I/ [HA1 K = [S-][BX+]/ [BI
acid HA base
BH’
photodetection of absorbing species (X) Q = eZKls [XI I exp[-(e1/2)[Xll product (charged species) absorbing Q , = a(z - 1)’Iz exp[-a(z - l ) ] extrema at azo2- (1 + a)z, + 1= 0 reactant (AH or B) absorbing extrema’at az,3 - 2 ~ 2 , ’t ( a - l ) z , - 1= 0 [I = elK/4 z = (1 + 4C,/K)”’ TABLE 11: Predicted ASIN
0.01 0.10 0.50 1.o 1.24 1.50 2.0 5.0 10.0
0
CKl:
A c i d Concent rat i o n ,
FIQXO 1. Effect on slgnal-tc-noise ratlo by the additbn of a strong acid. The curves represent different dye concentratlons, expressed as multiples of the dissociation constant K .
The importance of Ioin enhancing SIN has already been mentioned. The term elK in eq 14 appears in both the exponential and preexponential portions of the equation and thus is quite important in determining the magnitude of 6SIN. 6KIK = (K(E) - K(O))/K(O) is just the change produced by the Wien effect. Lastly, the curly braces in eq 14 contain all the concentration dependence, and it is this expression that we wish to examine more closely. We first examined the effect of adding acid to the system, that is, the effect of y upon 6SIN. It can be shown that the variation [d@S/N)/dy], = 0 leads to a sixth-order algebraic equation in y which could in principle be solved numerically. Instead we have chosen a graphical approach to illustrate the behavior of 6SIN as C, is varied. Figure 1 is a plot of 6SIN vs. C,/K for a series of concentrations C,. What the curves suggest is that the addition of acid sometimes results in a modest enhancement of &SIN, but the largest proportional increases occur a t very low dye concentrations, that is, in cases where 6SIN remains small regardless of acid concentration. Bearing in mind that an acidified medium will show an increase in ionic strength (and hence more ohmic losses during the E-jump pulse), and in view of the rather minimal effect on 6SIN from acid addition under the best of circumstances, we decided to further simplify eq 14 by considering only cases where C, = 0, that is, where y is set equal to unity. We then have
6S/N
(2)
’/’ 6K -a-
(2
K
- 1)’ (z)
exp( - %(z - 1)1)
(15)
with z (1 + 2x)’/’, a elK/4. Taking the natural log of eq 15 and differentiating with respect to z leads to the cubic equation
+ (a - l)zo - 1 = 0
azo3- 2azo2
(16)
This equation can be solved either analytically or numerically (if a is given). The solution gives the dye con-
a
1.020 1.183 1.732 2.236 2.441 2.645 3.00 4.683 6.403
- Q for Methyl Reda 0.0003 0.019 0.175 0.276 0.286 0.277 0.233 0.024 0.00015
0.0009 0.24 0.60 0.97 1.00 0.97 0.82 0.084 0.0005
a = 0.68, pK, = 5.05.
centration which results in an extremum for 6 S / N , and in particular a maximum when zo represents a physically realizable concentration, that is 20’
= 1 + 4Co/K
>1
Summary of Amplitude Analysis Equations 15 and 16 represent the results for dissociation of a weak acid, assuming photodetection of species [HA]. This is just one of four possibilities, depending on whether the indicator is acidic or basic, and which species is being monitored. Table I summarizes the conclusions for the four cases. In this table only the concentration dependence of 6SIN is retained; it is written in the form Q(a,z),where
6S/N
(I,/Av)1/2(sK/K)Q(a,z)
(17)
The solvent, designated SH, need not be water, but it is assumed to be autoprotolytic:
SH = S-
+ H+
K, = [S-][H+]
It can be seen from the table that the dye concentration required to obtain a maximum response with, e.g., [A-] as the detected species will in general not give a maximum response when [HA] is being monitored. To get some idea of the magnitude of SIN changes with concentration, we took known values for the indicator dye methyl red in aqueous solution. Both e and K are known, and 1 is the fixed path length between the quartz windows in the cell. This fixes a at 0.68, and the maximum effect is predicted (via eq 16) to occur at Co/K = 1.24 or Co = 14 p M , which is close to, but below, the solubility limit for methyl red in water. Table I1 shows the variation in Q as the magnitude of Co changes. Table I11 displays the variation of , Q with different a values. It can be seen that, as a increases, Q,, increases,
2488
The Journal of Physical Chemistry, Vol. 87, No. 14, 1983
TABLE 111: Variation of Qm, a 0.1 0.5 0.68' 1
( C ~ I K ) Q ~ , Qmax 4.80 1.52 1.24c 0.97
0.16 0.26 0.28 0.32
a = EIK. Methyl red. corresponds to C, = 1 4 1 M .
with a' a
(Co/K)Qmax
Qmax
10 lo2 103
0.25 0.073 0.023
0.51 0.65 0.70
For methyl red, this ratio
approaching an asymptotic limit. There are, of course, practical limits on the parameters which make up a, but the table suggests that any dye with a large a value should show a consequent increase in an optically detected Wien effect. The following points summarize the results of this section: (1)When one monitors small light-level changes, the quantity to examine is the signal-to-noise variation, 6S/N. (2) The gain of the PMT can be decreased to admit more light without saturation; this results in an increase in SIN proportional to P. (3) The concentration Corequired to maximize 6S/N is given by a cubic equation (HA absorbing) or a quadratic equation (A absorbing) relating Co to E and K. (4) The Wien effect will be significant only for a range of concentrations close to the optimum value. However, this optimum generally occurs close to Co = K. Hence, if an electrolyte becomes too weak, the maximum amplitude will occur at such great dilutions that no effect will be observed experimentally. Experimental Section The instrument is essentially the same as that described by Eyring.8 The high-voltage pulse was generated by connecting a charged HV capacitor (Plastic Capacitors Co., 0.005 pF, 60 kV) to the cell by means of a triggered spark gap (EG&G GP-15). After a predetermined time of a few microseconds, a second spark gap (SG-2) is fired to ground the cell. Details are covered in Eyring's paper.8 Ringing was usually observed on the leading edge of the pulse. The trigger transformers were EG&G Model Tr1700's. They supplied a high-voltage pulse to trigger the SG electrodes. The transformer secondary circuit of the spark gaps was analyzed as a possible source of the ringing that appeared on the leading edge of the pulse. The analysis was kindly provided by Victor Kuchinsky of New Jersey Institute Technology's Electrical Engineering Department. It showed that the current through the trigger electrode would be damped sinusoidal oscillations at a frequency of about 400 kHz. While this result was in qualitative agreement with the ringing frequency, the observed period was about 1 ps. In fact, the shape of the leading edge of the pulse was found to be rather sensitive to the exact values of the resistors in the circuit. Presumably the lumped inductance of the spark gaps, the high-voltage capacitor, and the other large circuit elements resulted in the damped, LC oscillation which was never completely eliminated. Depending on interelectrode spacing, the instrument could generate fields of up to 120 kV cm-'. The detector consisted of a fiber-optic light path from the quartz window of the cell to an rf-shielded photomultiplier. The PMT interfaced directly to a variable resistor mounted on the oscilloscope input, thereby eliminating any cable between the detector and oscilloecope. (8) Olmn, 5.L.;Silvr, R. L,;Holmw, L. P.; Auburn, J. J.; Warrick, P., Jr.; Eyring, E. M. Rev. Sci. Inetrun. 1971,42, 1247.
Rhinesmith and Hemmes
This configuration minimized input capacitance and ensured that the detector system would utilize the full 100MHz bandwidth of the oscilloscope, a Tekronix Model 7633 storage unit with rf shielding. The light sources employed included a 150-W xenon lamp, or alternatively a 150-W tungsten-halogen bulb. Some experiments used a Spectra-Physics argon ion laser at the 514-nm line. The greatly enhanced light levels of the laser improved the signal-to-noise ratio by a factor of about 100. Before the experiment was caried out, it was necessary to decrease the sensitivity of the PMT (to avoid saturation). This can be accomplished by shorting the higher dynode stages of the PMT to the anode and/or by lowering the high voltage between anode and cathode. We chose to operate the tube at a reduced voltage, typically around 450 V rather than the rated 950 V,. This reduced the gain of the PMT to within acceptable operating limits for the more intense light source. Had it been necessary to measure very short relaxation times on the order of a few hundred nanoseconds or less, undoubtedly a better approach would have been to short out the dynode stages. At no time did our chemical systems exhibit these short relaxation times, so we opted to leave the PMT intact, and thus readily adaptable for low light-level measurements. The current from the PMT establishes a voltage across a small resistor in parallel with the oscilloscope input. We employed a variable resistor, typically 1000-3000-R settings, giving rise to a PMT saturation current (1 mA) equivalent to an input signal of 1-3 V, with a maximum s. RC time constant of about 5 X Methyl yellow (MeY) was obtained from Aldrich Chemical Co. and recrystallized from ethanol (mp 109 "C). Glacial acetic acid was distilled before use. Methyl red obtained from Eastman Kodak was recrystallized twice from ethanol. Using the laser source revealed difficulties with aqueous samples. Fluorescence was often observed with distilled or deionized water. This could be reduced only by double distillation of deionized water from alkaline permanganate. In order to test the E-jump device it was necessary to run a known system. Aqueous methyl red was chosen, since it had previously been studied by Cole,gits protonated form had a maximum absorption at 520 nm, close to the laser output, and the amplitude analysis predicted a maximum Wien effect within the solubility range of the compound. The reaction times were analyzed in the same way as Cole,g that is 7-l
= k,([H+] + [MR-I) + k d
where T is the observed relaxation time, k, and kd are the recombination and dissociation rates, respectively, [H+] is the equilibrium proton concentration, and [MR-] is the concentration of methyl red anion. Our estimates of 12, and kd are as follows: k , = 5.45 X lolo M-' S-', k d = 4.30 X lo5 s-l, giving a pKa = 5.10. Cole's results were k , = 3.5 X 1O'O m-l S-', k d = 4.8 X lo5 S-l, pK, = 4.86. The spectroscopic pKa is 5.05. We consider this very satisfactory agreement. Results Methyl yellow is a weak base which when dissolved in glacial acetic acid is protonated. Spectroscopic evidencelo (9)Cole, D. L. Doctoral Dissertation, University of Utah, Salt Lake City, UT, 1970. (10) Snatzke, G.;Snatzke, F. 'The Chembtry of the Hydrazo, Azo,and Azoxy Group#";Patai, Saul, Ed.; Wiley: New York, 1976.
The Journal of Physical Chemism, Vol. 87, No. 14, 1983 2489
Dye Dimerization in Glacial Acetic Acid
d“
I
I
LOG
I “ u AS1d 0 LIGHT INTENSITY,
I
I
Flgwe 2. Wien effect in lo4 M methyl yellow in HOAc; the two traces representthe PMT output for the same sample at different time scales: 5 and 10 ps per horizontal division. Increased light intensity appears as more negative-going (downward) voltages. The field is turned on at the rise of the pulse, and tumed off just prior to the sharp drop. The light source is an argon ion laser (514 nm, 100 mW); the in-field absorption increase corresponds to an increase in the protonated form of the dye.
suggests that the azo group is the site of protonation rather than the dimethylamino group. In the concentration range 6-250 pM a relaxation process was observed by using either the xenon lamp or the laser. At high light intensities, however, a second relaxation was observed, lasting on the order of 5&100 ps. The double relaxation process is shown in Figure 2. It is seen that the second relaxation causes a decrease, or “dip”, in absorbance below the initial value. Changing the field strength by varying the electrode spacing showed the relative magnitude of the dip to be independent of field (that is, the ratio of the dip magnitude to the increase in absorbance due to the Wien effect was constant). No variation in instrumental parameters was found to alter this dip except the laser light intensity. The amplitude of the Wien effect-the initial absorption, before any bleaching took place-was found to be directly proportional to the laser light intensity over 2 orders of magnitude as shown in Figure 3. There was however a threshold light intensity above which the dip was observed. It should be pointed out that an electronic shutter was employed to completely block the laser output between experiments, so that the cell was illuminated only a few seconds before and after the application of the field. Using the laser light power and the absorbance of the solution, one can estimate a maximum temperature increase; it was calculated at 3 X lo4 “C s-l for a G c m 3volume, assuming a specific heat equal to that of solvent. We concluded that the evidence favored a change occurring in the excited state of protonated MeY. If BH+ represents protonated methyl yellow, it may be that BH+ + h~~~~ --.L (BH+)* nonabsorbing species
-
There are several possibilities for the product shown in the above scheme; most are inconsistent, however, with the time scale associated with the process. For example, there seems to be no evidence that MeY should have a particularly long-lived excited state, since there is no observed fluorescence or phosphorescence. One possibility is for the excited state to promote the formation of the amino-protonated tautomer
BH+ (azo) * BH+(amino) which does not absorb at 614 nm.l0
(1)
Flgure 3. Magnitude of the Wien effect with increasing light intensity. The arrows represent the light level at which a noticeable “dip” first appears.
Another bleaching mechanism might be excited-state isomerization
In cis-BH+ the phenyl rings are no longer coplanar,loand the .Ir-electron system of the azo nitrogens is no longer conjugated with the rings. Equation I is probably eliminated by considering the excited-state pK, change of azobenzene. The azo group becomes 17 orders of magnitude more basic in the excited state.ll Although the magnitude of this change need not be duplicated in MeY, there are strong heuristic arguments for assuming that the excited state of the base B would be higher in energy than the protonated form (B absorbs at a shorter wavelength). The transition to the protonated form would have to be accompanied by a simultaneous loss of excitation energy. Implicit in this discussion is the notion that protonation a t the amino group would be accompanied by deprotonation a t the azo group. The other possibility mentioned above, cis-trans isomerization of the excited-state molecule, must be given serious consideration. Azobenzene derivatives have been shown to undergo cis-trans isomerization quite readily,12 whereas the ground state for para-substituted azobenzenes is believed to be predominantly trans and to undergo little conversion. The photochemical isomerization of azobenzenes has been the subject of considerable investigation. Certain p,p’-substituted azobenzenes have been studied by flash spectroscopy.13 In this case the flash initiated an excess of cis isomer, and the relaxation after the flash was monitored. The rate of decay varied with solvent, tending toward faster rates in polar solvents, with the faster relaxation times on the order of milliseconds. Reference 13 also contains the observation that, when 4-(diethylamino)-4’-nitroazobenzeneis irradiated with visible light in various nonpolar solvents, a short-lived bleaching is observed, and “in more polar solvents such bleaching occurs but its duration is so short that a flash spectroscopic technique must be employed to follow the kinetics of relaxation”. It is a t least possible, then, that the in-field bleaching that we observed in MeY represented a cis-trans isom(11) Ireland, J. F.; Wyatt, P. A. R. “Advances in Physical Organic Chemistry”;Gold, V., Ed.; Academic Press: New York, 1976; Vol. 12. (12) Drewer, P. J. “The Chemistry of the Hydrazo, Azo, and Azoxy Groupr”;Patai, Saul, Ed,; Wilsy: New York, 1976, (19) Wilder, P,D,; Pacifici, J,0.;Irich, G,, Jr.; Whitten, D. G. J. Am. Chem, SOC,1971, fig, 2004.
2490
Rhinesmith and Hemmes
The Journal of phvslcsl Chemisby, Voi, 87, No. 14, 1983
TABLE IV: Relaxation Times for Methyl Yellow in Acetic Acid
TABLE V: Equivalent Conductivity for Methyl Yellow
in Acetic Acid A , mho
A , mho
104C,, M
M-* cm-'
A C ~ ~104C,, / ~ M
cm''
AC,1'2
0.1765 0.1166 0.1087
0.1343 0.1635 0.2155
M-I
~
6.3 22.5 56.3
3.61 ( 3 ) 3.11 ( 7 ) 2.40 ( 9 )
0.277 0.322 0.417
100
2.01 ( 7 ) 1.39 ( 3 ) 1.26 (11)
200 250
0.498 0.719 0.794
erization occurring in the excited state. After the field was turned off, the excess cis isomer persisted (resulting in a depletion of absorbing trans isomer), and then the bleaching effect eventually returned to equilibrium with ambient light conditions and zero-field concentrations. The magnitude of the dip was small, and the observed relaxation was not easily quantifiable, but under fixed conditions (concentration, light level) any dip was quite reproducible. We can summarize our findings, then, on the longer relaxation time found in MeY as follows: (1) After the initial rise in BH+ caused by the Wien effect, a bleaching, or decrease in absorbance, was observed. (2) The extent of the bleaching was reproducibly related to light intensity, and to virtually no other parameter (at high light levels all solutions over the entire concentration range showed this second relaxation). (3) Among the processes considered, photoinduced isomerization seems to be the most likely cause of the relaxation.
Faster Relaxation in MeY The photoinduced bleaching of methyl yellow can be suppressed or eliminated by reducing the light level and by employing shorter field widths. About 5 gs is sufficient time to complete the shorter relaxation, and it is much shorter than the photoinduced effect. Some of the SIN advantage of the strong light source was thereby lost, but the large Wien effect permitted reliable data to be gathered for a wide range of dye concentrations. Before analyzing the kinetics, we should emphasize that MeY in glacial acetic acid represents a very different solute-solvent system than, e.g., methyl red in water. For one thing, proton-transfer reactions of the form
SH + B
S-
+ BH+
(111)
Ki
Kd
+ BH+
(IV)
where the ionization equilibrium constant, Ki, is much greater than the dissociation constant, Kd, and the dots indicate hydrogen bonds. In other words, there is usually no free base, and most of the ions are joined into parts or higher aggregates. Even in aqueous solutions (nD = 78) azo dyes have been studied at similar concentration levels, and aggregaton has been reported.14 The much lower dielectric constant of HOAc should help stabilize the formation of both triplet-ion and quadrupole species, and possibly even higher aggregates.
as 2B = B2
(14) Yasunaga, T.;Nishikawa, S. Bull. Chem. Soe. Jpn. 19728 45,1262.
(V)
(i.e., dimerization of two bases), because no charge separation takes place. Naturally, whatever elementary processes are directly perturbed by the field, they may in turn be coupled to other reactions whose equilibria need not be field dependent. Second, certain processes are excluded by the nature of the solvent system. The elementary reaction shown in eq 111, for example, is ruled out because virtually all solute molecules participate in hydrogen-bond interactions. Our first expectation was that the kinetics would follow the process described by eq IV, repeated here with rate constants shown
-
B*.*HS
-
BH+**.S-
k2
BH+
kl
+ S-
(IV')
where S- is the acetate anion. The equilibrium constants for ionization and dissociation were found by Koltoff to be6 Ki = k4/kz = 0.10
Kd = k l / k 1 = 5
X
lo4 M-]
The relaxation times for the two-step equilibrium IV' are derived in standard texts.15 They are (7+,-)-'=
C K / 2 + [(CK/2)2 - nKI1/'
(18)
where
CK
kl([BH+]
+ [S-1) + k-1 + kz + k-2
n K = k l ( k 2 + k2)([BH+]+ [S-1) + k-lk-z The problem with eq 18 is that neither of the two relaxation times predicts the observed concentration dependence for 117 vs. c. The concentration behavior of [BH'] + [S-] is essentially a square-root dependence. When the data are plotted as 1/7 vs. c1I2, however, the line shows a noticeable upward curve, and the least-squares fit of the data gives a low correlation coefficient compared to other power law plots. At best the greatest concentration dependence arises when the disciminant in eq 18 vanishes. Then the process reduces to a single relaxation time 7-*
Experimental Results for Methyl Yellow The concentration dependence of the out-of-field relaxation is given in Table IV. It can be seen that a significant change in 7 with concentration takes place.
57.9 197 393
To interpret these results we have at ow disposal at least two other important considerations: First, the reactants and products of the perturbed species must be of differing charge. This is implicit in the nature of the Wien effect and immediately excludes direct examination of such steps
no longer exist as such in low-susceptibility, proton-donating solvents; instead, both base and protonated base exist as hydrogen-bonded complexes6 SH. * *Be S-. * .H+** .B e S-
0.0992 0.1215 0.1213 0.1270
0.5831 0.4974 0.3563 0.2361
2.90 5.79 11.58 28.95
= kle
+ (k-l + k 2 + 1 4 1 2
(19)
with 0 = (C/K#2 (15) Bernasconi, C. F. "Relaxation Kinetics"; Academic Press: New York, 1971.
Dye Dimerization in Glacial Acetic Acid
K2 = 1/Kd(Ki/(l
The Journal of Physical Chemistry, Vol. 87, No. 14, 1983 2491
+ Ki))
If 7-l is plotted vs. 0 and a linear dependence is assumed, there results slope = kl = 10.8 X 1O'O M-l intercept = (k1 + k,
+ k/,)/2
8-l
= 2.8 X
lo6 s-'
Now, kl represents a diffusion-controlled recombination rate which can be estimated from the Debye equation: l6 kl = kt = (8kT/3v)b/(l - exp(b)) b = e2/aDkT
(for a 1:l electrolyte)
Here e is the electronic charge, D is the dielectric constant, 7 is the solvent viscosity, and a is the ion-pair separation distance for BH+. a can be estimated from the equation for pair formation developed by Fuoss; l7 we find a = 6.00 A
k, = 8.2 X 1O'O M-' s-l in reasonable agreement with the experimental value. The value of the intercept, however, predicts much too low a value for the ionization rate constants. The intercept gives
+ k2 + k-2 = 5.6 x 105 8-1
k-l
and this implies k 2 and k-, must both be on the order of lo4 s-l or less (given the known value for Kd, klby itself is estimated to be 5.4 X lo6 9-9. These rates seem much too low for the ionization step, and they are not consistent with the assumption made to obtain a single relaxation time. Dye Aggregation Model Another possibility is to examine the kinetics of higher aggregate formation. Azo dyes tend to easily dimerize; lo in dimer and triple-ion formation the following equilibria all play a roll: pair formation MYH+ + OAC- = P, Kp
(A)
triple ion formation
P
+ MYH+ = T, KT
(B)
dimers from triples
T + OAc- = D, K,
bond with the solvent; for I to occur two H bonds must be broken to be replaced by the interaction energy of the two dipoles forming the quadrupole (I). Even though the dipole moment for MeY is quite large (2-3 D units in the ground state),'* this interaction energy can be estimated to be much less than typical hydrogen-bond formation energies of 5-10 kcal mol-l. Consequently, I11 is the type of dimer depicted in the scheme outlined above. Similar schemes have been proposed to account for the behavior of lithium salts in low-conductivity media where only partial dissociation occurs, and thus the salts must be considered weak electrolytes.6 The picture is one in which pairs and higher aggregates are the major species, and triple ions assume the majority role as charge carriers. Accordingly, although both equilibria A and C exhibit a Wien effect, equilibrium C plays a predominant role. To get quantitative estimates for this scheme, conductivity values as a function of electrolyte concentration are required. These measurements were taken for MeY in glacial HOAc at 20 "C, using a Beckman Model RC18A conductivity bridge, and the results are presented in Table
v.
The formation of triple ions and quadrupoles (dimers) represented by equilibria A-D has been examined in detail by Hemmedg and by Persoons.20 We shall outline the treatment here, without presenting detailed derivations. The object is to combine spectrographic, conductometric, and kinetic data to arrive at estimates for the equilibrium constants shown, as well as rates involved in the kinetic step(s). First, the all-over pair formation constant K, is obtained from spectral data (in this case). Second, the conductivity measurements are used to calculate KT, the triple-ion formation constant. Third, the kinetics of the field perturbation leads to an estimate of K,, as well as the rates for process C. Finally, with the three other equilibrium constants established, KQcan be found from the stoichiometric relationship Kd(e = KxKT (20) The second step, that of triple-ion formation from a monomer and a pair, generally involves two forms of triple ions. This is not the case for MeY, where it would be more likely for the base to remain as part of the aggregate, and for the smaller and mobile acetate ion to become detached. The equation used to estimate KT when only one species of triple ion is present was derived by Wooster:21
(C)
dimer from pairs 2P = D, KQ (D) where the I C s are the equilibrium constants for formation of the species on the right. The possibility of dimer formation in azo dyes at the micromolar level was investigated kinetically by Yasunaga and Nishikawa'l for congo red, using a T-jump apparatus. They found that a mechanism of the form of eq D would account for their results. In the case of a field-dependent equilibrium, however, mechanisms A and C would be selectively affected. It is possible, and indeed probable, that many forms of dimers occur in MeY-HOAc solutions; of interest here are the various "simple" dimers involving MeY (B) and acetic acid (AH): B, B (I); BAH, B (11); BAH,BAH (111). Of these species, the one presumed to occur most often is III. The most stable form of the dye involves a hydrogen (16) Debye, P. Tram. Electrochem. SOC. 1942,82, 265. (17) Fuoss, R. M. J.Am. Chem. SOC.1958,80, 5059.
Here A is the equivalent conductance, while Xo and A, are the limiting conductances of the monomer and triple ion, respectively. The rates of quadrupole formation from triple ions were calculated by using a general mechanism proposed by Persoons.22 By assuming an excess of triple over free ions one obtains T-' = k d + 2kf(KT/Kp)'/2~ (22) where kf/kd (=K,) are the formation and dissociation rates for the dimer in equilibrium C. To evaluate the constants, we used the all-over pair formation constant Kp from Kolthoff s data: Kp = 2.2 X (18) Yamamoto, 9.; Niahimura, N.; Haeegawa, S. Boll. Chem. SOC. Jpn. 1871,44, 2018. (1s)W a g , H. C.; Hemmen, P. J. Am. Chem. SOC.1878, 96,5119. (20) Persoona, A.; Hellmans, L. Biophys. J. 1978, 24, 119. (21) Wooster, C. B. J. Am. Chem. SOC.1937,59, 377. ( 2 2 ) Persoons, A., private communication.
J. Phys. Chem. 1983, 87, 2492-2502
2492
A
I
order of magnitude as those obtained for weak electrolytes in low-dielectric media: e.g., KT 102-103; K , 1 102.% The comparisons rely to a large extent on u trasonic measurements, but other techniques-5"-jump, for exampleyield similar estimates. K, tends to vary a good deal more than KB or KT, but the value of 5 X lo5 does not appear unreasonable. Lithium salts in various low-susceptibility solvents give K, i= 107-109 M-l.,* The rates calculated for dimer formation from monomer and trimer deserve comment; the main difference in the rates obtained for equilibrium C, as opposed to the rates calculated for equilibrium IV, is that, in the all-over kinetics for equilibrium C, we get linear behavior for 1/r with c, whereas in equilibrium IV we get (at best) a square-root relation. It is hard to propose a consistent mechanism leading to this concentration dependence without invoking some form of higher aggregation. The questions of the role of hydrogen-bond formation and tautomerization of the azo and amino nitrogens remain for further study. We have really sidestepped these issues by picturing a dimer of the form (BHA),; the internal structure of such a dimer may involve hydrogen bonding, azo/amino tautomers, or both.
7 -
.>I
L
50
io 0
WeY
is 0 concemtret.on
do0
azo
( / H )
Figure 4. Least-squares flt for 117 vs. concentration of M Y in WAC.
106 M-l. Analysis of the conductance data by the Wooster method gives KT = 138 M-l. Figure 4 shows the E-jump 1 / vs. ~ concentration data for MeY. The computed slope and intercept are slope = 2.13 X lo9 M-l s-l, intercept = 2.80 X lo5 s-l, so that kf = ( ~ l o p e ) / 2 ( K ~ / K ~=) '12.8 / ~ X 1O'O (M s)-l, in reasonable agreement with the computed diffusion-controlled rate of 8.2 X 1O'O (M s)-l. The ratio kf/kd = K, = 4.57 X lo5 s-l, and from the other three equilibrium constants
Acknowledgment. This research was partially supported by DOE contract no. OE-AC02-78ER14945, and by the Rutgers Univesity Research Council. The work comprised part of R.J.R.'s Ph.D thesis, submitted May 1982. Registry No. Methyl yellow, 60-11-7; acetic acid, 64-19-7.
KB = KT/Kx/Kp = 32 M-' Discussion The scheme for aggregate formation of MeY in HOAc represented by mechanisms A-D proved to be consistent with the experimental kinetic results and the conductance data. The derived values for KT and KQare of the same
(23) Saar, D. D. Doctoral Dissertation, Polytechnic Institute of New York, New York, NY, 1980. (24) Macanka, W. Doctoral Dissertation, Rutgers University, New Brunswick, NJ, 1981.
Electrochemical Reduction of an Isomeric Pair When the Products Interconvert Alan M. Bond' and KeRh B. Oldham'+ Division of Chemical and Physical Sciences, Deakin University, Wawn Ponds 3217, Vicforia, Australia (Received: November 15, 1982)
There is a commonly held view that structural change accompanying an electron-transferreaction leads to the observation of sub-Nernstian behavior. This may be reasonable if the straightforward mechanism ne + 01 s R2 is operative. However, if part of the "square" scheme
= RI
ne
t 01
ne
t 02 a R 2
It
If
applies, this conclusion is shown not to be generally valid. The converse thesis that Nernstian behavior implies structural integrity is also not generally correct. Reactions that are part of the square mechanism may cause a reversible electron transfer to appear irreversible by decreasing the slope of the reduction wave. But our treatment shows that they may equally well increase the slope or leave it unchanged. Under other circumstances the reduction wave may split into two, or become preceded by a gratuitous peak. The present study convinces us that drawing mechanistic conclusions from voltammetric data alone is fraught with danger. 1. Introduction
Considerable controveq has arisen in recent years Over claims of slow electron transfer being due to conformational changes.l It is often assumed that structural inferences can be drawn from the observation of reversibility, Permanent address: Trent University, Peterborough, Canada. 0022-3654/83/2087-2492$01.50/0
or the lack of it, in an electrochemical process.2 Thus if a species 01 is observed to undergo a reversible electroreduction, it is inferred that the product must be species Organometal. (1) C. P. Carey, Chem., L. 15b, D. Albin, c37(1978). M. C. Saeman, and D. H. Evans, J. (2) A. J. Bard and L. R. Faulkner, 'Electrochemical Methods", Wiley, New York, 1980, p 114.
0 1983 American Chemical Society
