Rate-Controlled Adsorption of Product in Stationary Electrode Polarography Matthew H. Hulbert and Irving Shain Department of Chemistry, University of Wisconsin, Madison, Wis. 53706 The theory of stationary electrode polarography has been considered for the electrochemical system, k.
0 f ne
R F! Rads,in which a reversible charge trans-
the Fick’s law boundary value problem for the stationary electrode polarography experiment with diffusion to a plane is
kd
fer is followed by a rate-controlled adsorption-desorption involving the product of the electrode reaction. The boundary value problem for the stationary electrode polarographic behavior was solved. Two limiting cases were also defined: one in which there is no significant diffusion of the product from the vicinity of the electrode, and one in which the concentration of the reactant is approximately constant during the experiment. Cyclic scan stationary electrode polarography was used to study the methylene blueleuco-methylene blue system in buffered (pH 6.5) ethanol-water solution. The logarithms of the potential independent adsorption and desorption rate constants were 10.5 f 1.0 [(mole/liter)-* sec-’1 and 1.67 *0.17 [sec-’1, respectively, and the potential dependent parameter was 0.5 i 0.1.
THEROLE OF ADSORPTION in stationary electrode polarography has been considered by a number of workers (I-@, and an extensive theoretical treatment presented (6) for the equilibrium adsorption case. This theory indicated that equilibrium adsorption coupled with reversible charge transfer can enhance the normal diffusion-controlled peaks or cause the appearance of additional peaks. The theory was evaluated in a study of the reduction of methylene blue to leuco-methylene blue, a system in which the product is strongly adsorbed and a prepeak is observed (7). At low scan rates, the behavior was that predicted for equilibrium adsorption obeying the Langmuir adsorption isotherm, coupled with reversible charge transfer. However, at higher scan rates, the experimental results suggested that a rate-limiting adsorption-desorption process might be involved. In this work the effects of kinetic adsorption and desorption of the product of a reversible charge transfer in stationary electrode polarography were considered, and the theoretical results were compared with those obtained experimentally using the methylene blue system. RIGOROUS TREATMENT FOR ADSORPTION AND DfFFUSION
Boundary Value Problem. For the reversible reduction of species 0 to species R followed by kinetic adsorption of R, 0
+ ne
k.
R i3 Rads
(1)
kd
(1) A. M. Mirri and P. Favero, Ric. Sci., 28, 2307 (1958). (2) W. Kemula, Z . Kublik, and A. Axt, Roczniki Chem., 35, 1009 (1961). (3) P. Delahay, “Double Layer and Electrode Kinetics,” Interscience, New York, 1965, pp. 53 ff. (4) A. M. Hartley and G. S . Wilson, ANAL.CHEM., 38, 681 (1966). ( 5 ) S . Srinivasan and E. Gileadi, Elecfrochim. Acfa, 11, 321 (1966). 39, 1514 (1967). (6) R. H. Wopschall and I. Shain, ANAL.CHEM., (7) Ibid., p. 1527. 162
0
t
2
0, x = 0 :
CO
- E”)]
= exp [(nF/RT)(E
(6)
C R
Here I? is the concentration of substance R on the electrode surface, rsis the surface concentration at saturation, and the other terms have their usual significance (6). The ratecontrolled adsorption-desorption process is reflected in Equation 5 , where the fluxes of species 0 and R are not equal, because of the accumulation of substance R on the electrode surface; and in Equation 7, in which the Langmuir kinetic adsorption equation is used to describe the rate of change of the surface concentration of substance R. This relatively straightforward electrochemical boundary value problem is complicated by two factors. First, the potential in Equation 6 is a triangular-wave function of time (6) O_ 2. The slope of this linear portion of the plot is a function of U. A complete characterization of the kinetic adsorption peaks would require extensive calculations of these or other appropriate working curves; this approach must be used whenever diffusion interacts with the adsorption-desorption processes. However, where diffusion can be separated from the adsorption-desorption processes experimentally, an approximate theoretical approach was developed which provides straightforward correlations between experimental and theoretical parameters. APPROXIMATE TREATMENT FOR ADSORPTION When the adsorption is strong, the solution concentration of species R at the electrode surface is very small in the kinetic adsorption case. Thus, the amount of species 0 consumed at the electrode to produce K in the solution is also very small. Species 0 is also consumed to produce R in the adsorbed state, the amount consumed being limited by the saturation surface concentration, rs. If the concentration of species 0 is high enough so that it is not significantly depleted during the time required to scan the adsorption-desorption peaks, simplification can be made by introducing the approximation t 2 0, x = 0:
CO
eo*;
CR
0
(25)
When this approximation is applied to the boundary value problem for kinetic adsorption, the diffusion process need no
I,&
(volts)
Figure 6. Theoretical stationary electrode polarograms for adsorption-desorption prepeaks Effect of saturation surface concentration, P. Parameter values as in TableI, except A , Fa X 0.5; B, X 1; C , X 2.5
longer be considered. The system of equations to be solved includes Equations 3, 6 to 12, 23, and 25. In general, the properties of the system which are of interest involve the current maximum of each adsorption peak. The maximum current can be determined by setting the derivative of the current equal to zero and evaluating the resultant equation. From Equation 12, the current is directly proportional to the flux of species 0 which, in turn, is equal to d r / d t (Equation 23). Thus, the current maximum occurs when the second derivative of the surface concentration with respect to time is equal to zero.
The differentials with respect to time in Equation 26 can be obtained from Equations 6,7, 10, and 11 to give
L
where the sign taken with a is negative for cathodic scans and positive for anodic scans. Equation 27 can be solved analytically for certain limiting values of the kinetic parameters. From the solutions, the characteristics of the stationary electrode polarograms-peak potential, peak height, and peak width-can be obtained in terms of the kinetic parameters. Three limiting cases were considered-rapid adsorption and desorption, slow desorption, and slow adsorption-and equations relating the peak characteristics to the kinetic parameters were derived for each case. These equations apply only when the approximation expressed in Equation 25 holds-that is, when the concentration of species 0 at the electrode surface is essentially constant. Scan Rate Slow with Respect to Rate Constants. The first limiting case occurs when the scan rate is slow with respect to the adsorption and desorption rate constants at
ANALYTICAL CHEMISTRY, VOL. 42, NO. 2, FEBRUARY 1970
165
Table 11. Peak Widths for Equilibrium Adsorption of Product from Rigorous Solution to Boundary Value Problem and from Approximate Treatment uFIRT, mv-l nAEwSamv nAEWsb mv 0 ... 90.6 0.01 71 72.1 55 50.4 0.03 0.05 40 39.7 0.10 25 25.4 0.20 14.5 14.8 0.30 9.9 10.4 0.40 7.5 8.03 a From (6). b Approximate treatment.
the peak. Under these conditions all of the terms involving (&a) drop out of Equation 27, leaving
o=
-ka2CR2(ra-
r) +
kakdCRr
- kakdCR(I" - r) 4-kd2r
+
K', predicts proportionality to (u e-u). Because of the way these functions enter into the relations, the differences in the effects on the peak potential are relatively small, Equation 33 also indicates that the peak potential is not a function of rs or ( + a ) but is a function of u. In agreement with Equation 33, Wopschall and Shain reported that the peak potential was a function of I" and ( & a ) only when species 0 was partially depleted at the electrode, a condition precluded by Equation 25 in the approximate treatment presented here. But contrary to Equation 33, Wopschall and Shain reported that the peak potential was independent of U . This conclusion resulted from coupling of parameters u and K' in the numerical calculations of (6). Since, in Equations 31, K is a function of u and CRis not, changes in u will be reflected in changes in the peak potential, the potential at which Kis equal to CR. The other two characteristics of the theoretical curves, the peak height and the peak width at half height, can be obtained from the Langmuir adsorption isotherm and Equation 23, since
(28)
at the maximum of the current-time curve. Equation 28 may be solved for the concentration of R at the peak maximum, ( C d p = (kd/ka)prp/(rs- P I P (29)
(34) The peak height is obtained by substituting the condition at the maximum expressed in Equation 31 into Equation 34
Equation 29 may be rearranged to
or, in terms of the current function, which is the Langmuir adsorption isotherm, as expected. This limiting case is one that Wopschall and Shain (6) examined in detail using computer solutions to the rigorous boundary value problem, and the results of this approximate treatment can thus be compared with the results reported previously. If the Langmuir adsorption isotherm describes the surface concentration of species R in the adsorbed state, Equation 7 can be replaced by the isotherm. Then, on carrying through the derivation, the maximum in the current time curve is found to occur when
CR
K
(31)
Substitution of this result into the isotherm shows that
(X0)P
=
-rs(+a1/2)(1
+
U)
4co* d nDo
Equation 35 indicates that the maximum flux, and therefore the peak current, is independent of the bulk concentration of the reactant when the concentration is maintained constant at the electrode, as reported previously (6). When the flux is normalized by Equation 17 to obtain the current function (Equation 36) for comparison with previously reported results the peak height is inversely proportional to Co*. The peak width at half height is obtained by determining the potentials at which the flux is one half that at the peak. Equating one half the peak flux from Equation 35 to the flux given by Equation 34 and dividing by terms common to both sides of the equation gives
r p = rs/2 as previously deduced from the shape of the calculated adsorption-desorption peaks (6). The peak potential can be calculated by substituting Equations 25, 6, and 9 into Equation 31. If Eo is identified with
(37) The two roots of Equation 37 obtained from the quadratic equation formula occur at potentials differing by
nAE, = 3.526 RT/[(l
Eli2
Ep
-
RT E112 = In (Co*/K') nF(u 1)
+
(33)
The change in the peak potential with changes in Co* predicted from Equation 33 is the same as that predicted from Equation 44 of (6) [after a recurring sign error in the equations in (6) is corrected]. The behavior of the peak potential for changes in K' at large and small limiting values of u predicted from Equation 33 is the same as that predicted from Equations 41 and 40 of (6). For intermediate values of U, Equation 33 predicts the dependence of Ep on IC to be 1). On the other hand, Equation 42 proportional to ( U of (6), which was devised empirically to fit the numerical results for intermediate values of u ( U = 1 to 10) for changes in
+
166
ANALYTICAL CHEMISTRY,
+ u)Fl
(38)
Values of nAE, measured by Wopschall and Shain (6) from theoretical curves and values calculated from Equation 38 are compared in Table 11. According to Equation 34, changing the direction of the voltage scan changes only the sign of the flux, and not the magnitude. Therefore the prepeaks are symmetrical across the zero current function axis. In addition, they are symmetrical about the line E = E*. This can be shown by considering a flux that is some fraction of the maximum flux given by Equation 35. When this flux is equated to the right-hand side of Equation 34, the resulting equation (which corresponds to Equation 37) is not altered by replacing ( E - Ep) by - ( E - Ep).
VOL. 42, NO. 2, FEBRUARY 1970
Equations 33, 36, and 38, which give the characteristics of the theoretical curves in terms of the kinetic and experimental parameters, are expected to be valid if the rate constants for adsorption and desorption of the electrode product are large with respect to the scan rate and the concentration of reactant at the electrode is maintained at approximately the bulk concentration. According to Wopschall and Shain (@, the latter requirement is met when r s d < 0.22 C o * d E . Desorption Rate Constant Slow. The second limiting case occurs when the desorption rate constant at the peak is negligible with respect to the adsorption rate constant and the scan rate. Under these conditions all the terms involving kd can be neglected in Equation 27, leaving
o=
-~ (*a)kau cR(p - r) 2
k,(*U)CR(rs
- r) - ka2CR2(ra- r) (39)
This same equation can be derived from the approximate boundary value problem if Equation 7 is replaced by an alternate assumption
dr/dt = k,CR(r8 -
r)
(40)
Since the right-hand side of Equation 40 is never negative, the surface concentration of the adsorbed product can never decrease. Thus the assumption applies to the experiment in which the initial potential is anodic of the adsorption prepeak (where the electrode surface is free of adsorbed product) and the potential is swept through the prepeak region toward cathodic values. That Equation 7 should reduce to Equation 40 whenever (kd)pis small with respect to both (k& and (ha) is reasonable, since ka, CR, and I' increase and k d decreases as the potential is swept in a cathodic direction. Equation 39 can be rearranged to give CR at the electrode at the peak maximum
Obviously, the negative sign must be taken with the scan rate, corresponding to an experiment in which the potential scan is cathodic. The equation for the potential of the adsorption peak is derived by substituting Equations 25, 6, and 10 into Equation 41.
Equation 42 predicts results the same as those noted in the discussion of the rigorous solution of the abridged boundary value problem : The potential of the rate-controlled adsorption peak moves toward cathodic values as the scan rate or u increases and the bulk concentration or kat decreases. The peak height can be obtained by use of Equation 23, the rate equation for I' (Equation 40), and the condition at the maximum (Equation 41). Equation 40 is a first-order, linear differential equation and can be solved for r in a straightforward manner. If r is equal to zero at t = 0, the solution is
from Equation 41 into Equation 43 gives the surface concentration at the peak maximum
r p=
ryl
- e-l)
(4.4)
and therefore (45)
or, in terms of the current function,
The behavior predicted by Equation 46 is the same as that noted for the adsorption peak current function from the numerical results. In the same manner as for the first limiting case, the peak width at half height can be calculated by use of Equations 40, 43, and 45 as
nAE,
= 2.446 RT
+
(47) F(1 u/2) Thus, the peak width is a function of only n and u, as in the equilibrium adsorption case. Absorption Rate Constant Small. The third limiting case occurs when the adsorption rate constant at the peak is negligible with respect to the desorption rate constant and the scan rate. Under these conditions all the terms involving k, in Equation 27 can be neglected, yielding
As before, this equation for the condition at the peak maximum can be obtained by the alternate procedure of assuming in place of Equation 7 that
dr/dt = -kdr (49) Equation 49 is the complement to Equation 40 and applies to the experiment in which the potential is initially cathodic of the adsorption prepeak (where the electrode surface is saturated with adsorbed product) and the potential is swept through the prepeak region in an anodic direction. Substitution of Equation 11 into Equation 48 gives the desorption peak potential
According to Equation 50, the desorption peak moves toward anodic potentials as the scan rate increases and as ks' or u decreases. Unlike the kinetic adsorption peak potential, the kinetic desorption peak potential is independent of the bulk concentration. Since r equals rSat the beginning of the potential scan, substitution of Equation 11 into Equation 49 yields
Substituting the condition at the peak maximum (Equation 48) into Equation 51 and the resulting value of (r), into Equation 49 gives
or, in terms of the current function,
r(t)is proportional to the integral of the current and therefore to the area under the part of the adsorption peak produced in time t . Substituting the value of CR at the peak maximum ANALYTICAL CHEMISTRY, VOL. 42, NO. 2, FEBRUARY 1970
(53) 167
Thus the height of the desorption peak current function is directly proportional to I",u, and l/a, and inversely proportional to the bulk concentration. The desorption peak width at half height, calculated from Equations 11,49, and 52, is nAE, =
4.892 RT ~
UF
(54)
Application of Theoretical Results to Experimental Systems. If preliminary experiments show cathodic and anodic prepeaks that shift apart with increasing scan rate and are characterized by direct proportionality between the maximum current and the scan rate, cyclic potential scan experiments through the prepeak region, using a wide range of scan rates, could be used to characterize the system in terms of the theory of kinetic adsorption of the product. In these experiments, the solution concentration should be high enough so that depletion of the reactant at the electrode surface is not important. At low scan rates the prepeaks will have the symmetrical shape that is typical when adsorption-desorption equilibrium and the peak currents will be proportional is maintained to the scan rate. At a given scan rate, the adsorption and desorption peak potentials will be equal, the peak widths will be equal, and the magnitude of the peak currents will be equal. As the scan rate is increased and the kinetics of adsorption and desorption become rate-limiting, the peaks will become skewed and be shifted apart along the potential axis. The behavior of the peaks will be intermediate between the equilibrium and the kinetic behavior for about a five-fold change in the scan rate for the adsorption (cathodic scan) peak and for about a 50-fold change in scan rate for the desorption (anodic scan) peak. Above these transition ranges in the scan rate, the peak currents will again become proportional to the scan rate, but with new and differing proportionality constants. In addition, the adsorption peak will shift toward cathodic potentials in proportion to the logarithm of the scan rate, and the desorption peak will shift toward anodic potentials in proportion to the logarithm of the scan rate but with a smaller proportionality constant. If the scan rate is increased to the extent that the surface concentration is no longer maintained approximately equal to the bulk concentration, diffusion control will set in and the peak current for the adsorption peak will become proportional to the square root of the scan rate. Increasing the bulk concentration will cause the scan rate at which diffusion control sets in to be higher. The peaks can also be shifted apart with increasing scan rate due to the onset of diffusion control, even though the adsorption and desorption rates are not limiting. However, the characteristic behavior in this case is different from that expected when the adsorption and desorption rates become limiting. When diffusion control enters the equilibrium adsorption case, the adsorption peak current becomes proportional to the square root of the scan rate and the adsorption peak takes on the approximate shape of a diffusion-controlled stationary electrode polarography curve, while the desorption peak current remains approximately proportional to the scan rate and the desorption peak maintains its position and its symmetrical shape. If the variation with scan rate of the adsorption and desorption prepeaks corresponds to that outlined above for the kinetic adsorption case, information from plots of the characteristic quantities defining the curves, E,, i, and AEm,can be
(a,
168
used to determine the kinetic parameters, kat, kat, and U . From the curves obtained at a single concentration as a function of scan rate, the difference between the adsorption peak potential and the polarographic half-wave potential, AE,, and the difference between the desorption peak potential and the half-wave potential, AEd, can be obtained. Plots of AE, and AEd us. the natural logarithm of the scan rate will each consist of a horizontal line at low scan rates, a curved transition line at intermediate scan rates, and a second straight line at high scan rates. Similarly, plots of the adsorption and desorption peak currents and peak widths against the scan rate will consist of two straight lines joined by a transition curve. In the low-scan-rate (equilibrium adsorption-desorption) region, u can be obtained by substituting the intercept of the peak width plot into Equation 38, and K' can be obtained by substitution of the intercept of the peak potential plot and u into Equation 33. In the high-scan-rate (rate-controlled adsorption-desorption) region, u and k,' can be determined by substituting the slope and the intercept of the adsorption peak potential plot into Equation 43. Sigma and kd' can be determined by substitution of the slope and intercept of the desorption peak potential plot into Equation 50. Sigma also can be determined independently for both the adsorption peak and the desorption peak from the intercepts of the peak width plots, substituted into Equations 47 and 54. Sigma can also be determined from the ratio of the slopes of the peak current plots at high and low scan rates. For the adsorption peak, Equations 45 and 35 show that this ratio uj; and for the desorption peak, Equations is 2(2 u)/e(l 52 and 35 give the ratio as 2u/e(l u). The correlations between the characteristics of the curves and the kinetic parameters outlined above can be applied only to experimental systems which closely follow the mechanism upon which the boundary value problems are based. Thus, the experimental conditions must be arranged so that the adsorption is rate-controlled over a range of scan rates. The onset of diffusion control as the scan rate is increased is an important limiting factor in the application of these correlations. In some cases it may not be possible experimentally to observe the transition from equilibrium adsorption to kinetic adsorption because of interference of diffusion control at relatively low scan rates.
+
+
+
EXPERIMENTAL VERIFICATION
OF KINETIC ADSORPTION THEORY
An experimental test of the theory for stationary electrode polarography of a system involving kinetic adsorption of the electrode product was made using methylene blue, which was selected because the results could be compared with those obtained by previous workers (7, 13-15). The characteristics of the methylene blue system have been studied by Michaelis et al. ( I @ , and both the chemical and electrochemical properties of the system have been summarized (7, 12). The theory was tested using 0.10 and 0.17 m M methylene blue in pH 6.5 Britton-Robinson buffer. The solvent was 55 weight ethanol-water and the inert electrolyte was 0.5M (13) R. Brdicka, Z. Elektrochem., 48,278 (1942). (14) R. Brdicka, Collection Czech. Chem. Commwz., 12, 552 (1947). (15) W. Lorentz and E. 0. Schmalz, Z. Elekrrochem., 62, 301 (1958). (16) L. Michaelis, M. P. Schubert, and S. Granick, J. Am. Chern. SOC.,62,204 (1940).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 2, FEBRUARY 1970
~
~
(I
~~
Table III. Experimental Prepeak Characteristics for 0.10 mM Methylene Blue at pH 6.5 Scan rate, vlsec Epn0US. SCE, mv Ep,d us. SCE, mv b a , Ira i p , d , Ira AE,.., mv 0.042 - 107 -98 *.. ... ... 0.098 - 107 - 100 ... ... ... 0.232 - 107 - 102 .,. ... .., 0.457 -111 - 103 ... ... ... 1.07 -113 -99 14 - 16 46 -96 28 - 30 42 2.08 -112 -96 50 - 52 50 4.18 -118 - 123 -91 110 -112 51 9.71 20.7 - 133 -78 208 -218 55 23.2 - 136 - 74 212 - 230 58 46.7 - 151 - 58 356 - 373 63 111 -181 -22 621 - 650 80 203 -219 +12 1092 - 1016 95 +23 1016 - 982 98 233 -227 Estimated by extrapolation because of interference from current due to mercury dissolution. Table IV. Experimental Prepeak Characteristics for 0.17 mM Methylene Blue at pH 6.5 E,.,, us. SCE, mv E p , d , us. SCE mv ipsa,Ira ip,dt Ira AEWsa,mv -111 - 107 ... ... ... 0. loo -111 - 109 ... ... ... 0.200 -113 - 108 ... ... ... 0.467 -114 -110 6.4 -8.1 48 - 107 15 - 19 48 1.10 -117 - 107 31 - 37 47 2.20 -118 5.15 - 126 -100 54 - 68 49 - 138 -90 111 - 128 49 9.93 -135 51 10.8 -134 - 92 118 14.2 - 135 - 80 148 - 173 54 -216 62 20.1 -136 - 80 186 - 330 67 33.2 -154 - 66 305 -441 72 46.7 - 168 - 58 408 - 552 88 70.4 - 175 - 39 542 - 597 84 75.3 - 187 -49 577 -682 101 100 - 192 -23 697 -720 105 116 - 198 - 19 774 147 -222 -28 895 - 846 103 +2 1160 - lo00 126a 217 -239 Estimated by extrapolation because of interference from current due to mercury dissolution.
45 42 46 52 59 60 66 89 108 1120
Scan rate, v/sec 0.048
a
sodium nitrate. The concentrations were chosen so that the weak adsorption of the reactant could be neglected (7). Cyclic stationary electrode polarograms were obtained over the range in scan rate from 40 to 200 volts per second. Experimental Procedures. The chemicals, cell, and electrodes used in carrying out the experiments were similar to those used by Wopschall and Shain (7), except that the methylene blue (Merck, U.S.P. grade) was recrystallized from water. The controlled potential instrumentation has been described (17). The stationary electrode polarograms were recorded photographically from oscilloscopes, and all DIME polarograms were obtained with a Moseley 2D-2A X-Y recorder. The hanging mercury drop electrode radius was of the order of 0.6 mm. Experimental Results. From the stationary electrode polarograms, data on the shapes, heights, and potentials of the prepeaks and the diffusion peaks were obtained and compared with the characteristics expected from theory for a system in which the electrochemical product is strongly absorbed in a rate-controlled step. As predicted, the adsorption-desorption peaks at low scan rates were approximately symmetrical about the zero current axis and the peak potential. As the scan rate was increased, a point was reached where the adsorption peak began to shift toward (17) R. L. Myers and I. Shain, Chem. Ztutr., in press.
46 46 47 51 57
57 61 66 71 86 92 91 104
110 106 128"
cathodic potentials, and the desorption peak toward anodic potentials. The amount of this shifting along the potential axis increased with increasing scan rate. The adsorptiondesorption peaks became broadened, with the rising portions of the peaks having a lesser slope. With increasing scan rate the height of the adsorption-desorption peaks increased more rapidly than that of the normal diffusion-controlled peaks. All of these observations were predicted by the theory for the stationary electrode polarography of systems involving kinetic adsorption of the product. The only qualitative observation that did not follow these predictions was that a maximum appeared on the anodic diffusion peak. Because the adsorption-desorption peak is well removed from the diffusion peak, this caused no difficulty in making the measurements. The peak potentials, peak currents, and peak widths were determined from experiments performed in triplicate or quadruplicate (Tables I11 and IV). Because of the low concentration of the electroactive material, current measurements at the low scan rates could not be made accurately enough to be useful; however, all the peak potentials could be measured. Peak Current Behavior. At scan rates below about 25 volts per second, the peak current is approximately proportional to the scan rate (Figure 7), as expected for strong equilibrium adsorption. At higher scan rates the peak current falls away from the low scan rate limiting line. At these higher scan rates, the peak current is approximately
ANALYTICAL CHEMISTRY, VOL. 42, NO. 2, FEBRUARY 1970
169
.
I
IO00
..
Eo
(m V)
iL
50
0.01 100
0
I
I
1.0
IO
Figure 10. Difference between adsorption peak potential and polarographic half-wave potential, AE,, us. logarithm of scan rate for 0.1 mMmethylene blue
Figure 7. Adsorption peak current us. scan rate A, 0.17 m
I
v, (V/sec)
200
v, (V/sec)
Methylene blue. 0 , 0.1 mM;
I
0.I
M
.‘
I
I
I.
,001
*.. 0.I
. * * I
1.0
t
IO
IO0
v, (V/sec)
Figure 8. Adsorption peak current us. square root of scan rate for 0.17 mMmethylene blue
Figure 11. Difference between desorption peak potential and polarographic half-wave potential, A Ed, us. logarithm of scan rate for 0.1 mMmethylene blue
peak potential behavior quantitatively, a value of the polarographic half-wave potential, Ell2, was needed (Equations 9 to 11). The true half-wave potential in the presence of adsorption was measured at the current i = (id i,)/2 where id is the total diffusion current and i, is the prewave limiting current (18). The dropping mercury electrode polarograms included both cathodic and anodic scans; the half-wave potential was found to be -209 mv us. SCE. Figure 10 shows a plot of the difference between the adsorption peak potential and the half-wave potential, AE,, us. the logarithm of v. AE, is approximately constant in the low scan rate or equilibrium adsorption region and decreases in the higher scan rate region. A modified linear leastsquares computer program was used to obtain the slope and intercept of the line through the higher scan rate points. The slope was found to be - 10.4 mv with a probable error of 0.6 mv and the intercept (at log u = 0) was 106 mv with a probable error of 1 mv. The probable error is based on the assumption that the experimental error all lies in the determination of the y-coordinate (in this case, AE,). Figure 11 shows a plot of AEd us. log u. Again, the data points fall along two straight lines. In the low scan rate region, AEd is approximately constant and is 5 to 10 mv anodic of AE,. The least-squares analysis gives the slope of the higher scan rate region as 49.7 mv (probable error 0.9 mv), and the intercept as -42 mv (probable error 5 mv).
+
i 01
I
I
100
200
v, (V/sec)
Figure 9. Desorption peak current us. scan rate for 0.17 mM methylene blue
proportional to the square root of the scan rate for scan rates greater than about 50 volts per second (Figure 8), indicating that diffusion becomes significant at about this rate. The desorption peak current us. scan rate is plotted in Figure 9. The points fall along two straight lines as expected for a system at equilibrium at low scan rates and under kinetic control at high scan rates. The slope in the equilibrium adsorption region is the same for both the adsorption and the desorption peaks, as required by theory. The effects due to diffusion control observed for the adsorption peak are not expected for the desorption peak, since, in the latter case, the material participating in the electron transfer reaction is already present in the adsorbed state on the electrode surface. Peak Potential Behavior. To characterize the adsorption 170
(18) I. M. Kolthoff and J. J. Lingane, “Polarography,” Vol. I, Interscience, New York, 1952, p. 259.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 2, FEBRUARY 1970
Ref. This work
Table V. Kinetic Adsorption Parameters for leuco-Methylene Blue log k,'" log kdlb log K f C 10.5 i 1 . 0 1.67 f 0.17 -8.8 f 1 . 2
(13) (15) (7) a
-8
=1
. * .
..*
>8.3
...
...
-7.6
... & 0.3
U
0.5 f 0 . 1
... ...
0 . 4 f- 0.1
Standard state, (mole/liter)-l sec-1. Standard state, sec-I. Standard state, (mole/liter).
Discussion of Experimental Results. The coulometric value of n, 2, was used with the experimental slopes and intercepts to obtain the kinetic parameters. The value n = 1.66 used by Wopschall and Shain (7) to correct the shape of the diffusion peak for the presence of a reactive intermediate in the electrochemical reaction was not used, since the effect of the intermediate is diminished at potentials removed from the half-wave potential. Substitution of the slope and the intercept of the AEa plot into Equation 42 gives log k,' = 10.5 [(mole/liter)-l sec-'1, and u = 0.48. From Equation 50 and the slope and intercept of the AEd plot, log kd' = 1.67 [sec-I] and u = 0.52. The experimental error levels associated with these kinetic parameters is about 10% for the rate constants and 20% for the potential dependence parameter. This error level is not due primarily to the probable error calculated from the least-squares method, but rather to uncertainty in the choice of the proper points to which to fit the lines. The potential independent adsorption rate constant calculated from the low-scan-rate peak potentials (taking u = 0.5) is, within the error level, the same as the ratio of the potential independent rate constants recorded above. Agreement of these results with those reported earlier is reasonable (Table V). However, the internal agreement is somewhat disappointing. The proportionality constant between the scan rate and the adsorption peak current is expected to be about 20% higher in the kinetic region than in the equilibrium adsorption region of the scan rate, but no change in the proportionality constant before diffusion control enters is indi-
cated in Figure 7, probably because of mixed control by adsorption kinetics and diffusion. The experimental error in obtaining the peak widths is large, since each peak width is the result of several measurements, and therefore closer examination of the peak widths does not aid in determining if mixed control by adsorption kinetics and diffusion is in effect. Since the adsorption and desorption peak potentials are not the same in the equilibrium adsorption region, some diffusion control is indicated. Ordinarily, complications due to diffusion would be eliminated by increasing the bulk concentration; but the weak adsorption of methylene blue itself makes it impossible to use this method to increase the range of scan rates over which kinetic control is observed. Even with the difficulties due to the effects of diffusion, the results of the experiments indicate that the methylene blue system can be described in terms of a reversible chargetransfer reaction with the product strongly adsorbed in a ratelimited step. The theoretical treatment of the effects of kinetic adsorption and desorption on the stationary electrode polarographic experiment should be of value in the study of other experimental systems involving adsorption. RECEIVED for review August 29, 1969. Accepted October 24, 1969. Work supported by the National Science Foundation under Grant GP-3907. Other support received from the US.Atomic Energy Commission under Contract AT(l1-1)1083.
Use of Energy Transfer in Luminescence Analysis Determination of Aromatic Carbonyl Compounds Seth R. Abbott and David M. Hercules' Department of Chemistry and Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Mass. 02139 Long-range dipole-dipole energy transfer in fluid solution is discussed in relation to its use in chemical analysis. Specifically triplet-singlet energy transfer is considered for analysis of either the energy donor or acceptor of a given pair. Interferences are considered due to competing absorption, emission or energy transfer, as well as collisional quenching. An analytical method is described for the analysis of aromatic carbonyl donors by triplet-singlet energy transfer to a hydrocarbon acceptor. Specifically the benzophenone-perylene system is considered. The method has a limit of detection of ca. 10-%I and a % relative error of ca. =t2%. Using this method to monitor a peroxide decomposition reaction producing benzophenone a first-order rate constant of 3.18 & 0.17 x 10-5 sec-1 was obtained as compared to a rate constant of 3.42 ==! 0.21 x 10-5 sec-1 using phosphorimetry.
ALTHOUGH ENERGY transfer has not been utilized extensively in analytical chemistry, several examples have appeared in the literature. For example, Kreps et al. ( I ) have utilized energy transfer in crystalline anthracene to analyze for naphthacene impurities over a wide range of concentrations. Parker et al. (2) have used delayed sensitized fluorescence for the selective Present address, Department of Chemistry, University of Georgia, Athens, Ga. 30601. Address all correspondence to this author. (1) S. I. Kreps, M. Druin, and B. Czorny, ANAL.CHEM., 37, 586
(1965). (2) C. A. Parker, C. G. Hatchard, and T. A. Joyce, Analyst (London), 90, 1 (1965).
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