ORGANIZACIONES SOCIALES Capítulo

In order to compare the rate constants with one another, ideally both the

reorganization energies (λ) and electronic coupling elements need to be precisely known or need to be constant for the series of contacts under investigation. Since the

reorganization energy enters the Frank Condon factor (see Eq. 2.5) in the exponent, knowledge of λ is of outmost importance. The reorganization energies (λ) of selected Os-

polybipyridyl compounds were measured by means of NMR line broadening techniques23

for the same experimental conditions that prevailed during charge-transfer rate

measurements. The measurements were carried out in a pH 7.8 imidazole buffer (D₂O, 1 M KCl, deuterated imidazole + DCl) and in pH 5 buffer (D₂O, 1 M KCl, deuterated pthalic acid and DOH, ϑ ∼ 2 oC). The self-exchange rate constant (k_ex)of [Os(bpy)₂(4-

Meim)₂]3+/2+ (this is a protonated analog to [Os(bpy)₂(Him)₂]3+/2+) at pH 7.8 was (1.10 ± 0.33)×108 s-1, which corresponds to λ = 0.66 ± 0.04 eV. The self-exchange rate constant of [Os(bpy)₂(n-Meim)₂]3+/2+ at pH 7.8 was (1.02 ± 0.40)×108 s-1, which corresponds to λ =

0.65 ± 0.03 eV. The self-exchange rate constant of [Os(dmbpy)₃]3+/2+ at pH 7.8 was (1.09 ± 0.00)×108 s-1, which corresponds to λ = 0.65 ± 0.00 eV. The reorganization energy of [Os(dmbpy)₃]3+/2+ was re-measured in pH 5 buffer and gave the same result as in pH 7.8 buffer.

The values of λ are similar enough to allow for a direct comparison of k_et in terms of their electrochemical driving force and electronic coupling dependence. Selected k_et

Figure 2.8 Plots of Electron-Transfer Rate Constants (k_et) vs. Driving Force for Charge Transfer.

The determination of the rate constants is detailed in the text. The ∆Go’ values correspond to the barrier height values for equal accpetor and donor concentration ([A]=[A-]). The data used to generate the plots are summarized in Table 2.4. Circles correspond to redox couple I, triangles down corresponds to redox couple II, squares correspond to redox couple III, diamonds correspond to redox couple IV, and

triangles up correspond to redox couple V. (a) Data for ZnO1_I_pH8-

ZnO1_V_pH8 (filled symbols) and ZnO2_I_pH8-ZnO2_V_pH8 (open symbols). (b) Data for ZnO1_I_pH8-ZnO1_V_pH8 (filled symbols) and ZnO1_I_pH6.8- ZnO1_V_pH6.8 (open symbols). (c) Data for ZnO1_I_pH8 and ZnO1_IV_pH8 (filled symbols) and ZnO1_I_pH6 and ZnO1_IV_pH6 (open symbols). Arrows indicate the shift in k_et when the pH of the buffer is lowered.

∆G

o'

(eV)

0.4 0.5 0.6 0.7 0.8 0.9 1.0

k

et

(c

m

4

s

-1

)

10-20 10-19 10-18 10-17

I

II

III

IV

V

Figure 2.8 (a)

∆G

o'

(eV)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

k

et

(c

m

4

s

-1

)

10-20 10-19 10-18 10-17

I

II

III

IV

V

Figure 2.8 (b)

∆G

o'

(eV)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

k

et

(c

m

4

s

-1

)

1e-20 1e-19 1e-18 1e-17

I

IV

Figure 2.8 (c)

the k_et values for these two electrodes were somewhat different, the overall trend is comparable. The k_et values obtained for redox compound III were (20.9 ± 8.3)×10-19 cm4 s-1 (ZnO1_III_pH8, Φ_B = 0.573 ± 0.007 eV) and (20.9 ± 10.0)×10-19 cm4 s-1

(ZnO2_III_pH8, Φ_B = 0.617 ± 0.012 eV). The barrier height of this contact was similar to the reorganization energy of 0.66 eV and indicates that compound III operated close to the point of optimum exoergicity, see Eq. 2.5. The redox compound exhibiting the largest driving force for electron transfer, compound I, consistently gave lower k_et values than compound III: (1.0 ± 0.4)×10-19 cm4 s-1 (ZnO1_I_pH8, Φ_B = 0.900 ± 0.003 eV) and (2.7 ± 1.3)×10-19 cm4 s-1 (ZnO2_I_pH8, Φ_B = 0.944 ± 0.006 eV). Redox compound II followed this trend. Its rate constants, however, were slightly smaller than those of

compound I, see Table 2.4. The redox compound with the lowest driving force, compound IV, had rate constants similar to those of compound III, (8.8 ± 3.5)×10-19 cm4 s-1

(ZnO1_IV_pH8, Φ_B = 0.433 ± 0.003 eV) and (28.3 ± 13.5)×10-19 cm4 s-1

(ZnO2_IV_pH8, Φ_B = 0.467±0.001 eV). Given the structural similarities of compound V

and compound III and the similar driving forces for electron transfer, the rate constants obtained for n-ZnO in contact with V differed remarkably from those obtained for n-ZnO/ III: (0.7 ± 0.3)×10-19 cm4 s-1 (ZnO1_IV_pH8, Φ_B = 0.572 ± 0.010 eV) and (0.9 ± 0.4)×10-19 cm4 s-1 (ZnO2_IV_pH8, Φ_B = 0.467 ± 0.001 eV).

The observed trend for changes in k_et with pH are presented in Figure 2.8 (b) and (c). These experiments are especially interesting because they provide an alternative way of changing the driving force for electron transfer without changing the nature of the redox compound thereby keeping parameters like the electronic matrix element constant. In the case of electrode ZnO1 the observed dependence of k_et with pH seems to suggest that the rate constant of electron transfer from ZnO to compound I and II increased with

decreasing driving force. The rate constants for junctions ZnO1_I_pH6.8 and ZnO1_II_pH6.8 were (1.6 ± 1.0)×10-19 cm4 s-1 (Φ_B = 0.830 ± 0.014 eV) and (3.2 ± 1.8)×10-19 cm4 s-1 (Φ_B = 0.662 ± 0.006 eV). This trend was also observed for compound I at pH 6, see Table 2.4 and Figure 2.8 (c) (note that measurements at pH 6 and pH 7.8 were taken immediately after each other). With the exception of compound V, the reverse trend was observed for redox compounds with lower driving force. Compound IV showed a lower k_et at pH 6.8 and pH 6.0 than at pH 8, k_et = (2.1 ± 1.8)×10-19 cm4 s-1

(ZnO1_IV_pH6.8, Φ_B = 0.346 ± 0.007 eV) and (0.3 ± 0.2)×10-19 cm4 s-1

(ZnO1_IV_pH6.0, Φ_B = 0.269 ± 0.013 eV). For electrode ZnO2 not enough results are

available for a valid comparison of the rate constants. The measurements at pH 6.5 were taken after the electrode was repolished and this introduced a large shift in the flat-band potential and in the linear regression slope of the Mott-Schottky plot. A comparison of this data set with the rate constants at pH 8 therefore seems to be inappropriate.

Measurements at pH values smaller than 6.00 resulted in non-rectifying behavior for compounds with a low driving force, despite the fact that the driving force was still larger than 3 k_BT. At low pH values the surface of the ZnO electrode showed rapid signs of degradation, so measurements were restricted to pH values larger than 6.00.

2.4.5 Rate Constants of n-ZnO in Contact with [Fe(CN)₆]3-/4-, [Co(bpy)₃]3+/2+, or [Ru(NH₃)₅py]3+/2+

In an earlier part of this study the reorganization energy dependence of ZnO/liquid contacts was studied.47 The results of these measurements are presented in Table 2.5. The differential capacitance measurements showed ideal energetics. The junctions showed no frequency dispersion of the differential capacitance and the r2 value for Mott-Schottky plots was typically 0.999 or better. Electrode ZnO3 had a dopant density N_D = 8×1016 cm-

(ZnO3_VI_pH8.7). The crystallographic orientation of the crystals was determined by single-crystal X-ray diffractometry and no significant changes in the orientation were detected before and after repolishing. It should be noted that despite higher dopant densities and higher pH values, E_fb values are more positive than the E_fb values of ZnO1 and ZnO2.

With J-E measurements of n-ZnO/[Fe(CN)₆]3-/4- (compound VIII) contacts, we have confirmed previous reports14-16 on the adherence of this system to the ideal rate law. The n-ZnO/[Co(bpy)₃]3+/2+contact (compound VI) is another example of such an ideal system. However, the rate of interfacial electron transfer at n-ZnO in contact with [Ru(NH₃)₅py]3+/2+ (compound VII) was found to be independent of the acceptor concentration, which might indicate that VII adsorbs to the surface, for instance via hydrogen bonds to the hydroxylated surface of n-ZnO. The results for n-ZnO/[Fe(CN)₆]3-/

4- _{contacts, k}

et = (1.1 ± 0.6)×10-20 cm4 s-1 and ΦB = 0.6 eV, agree well with Morrison's

result of k_et = 3×10-20 cm4 s-1 and Φ_B = 0.7 eV. It is not clear whether [Fe(CN)₆]3-/4- can be used for further mechanistic studies of interfacial rate constants, since speculations about kinetic complications and cation effects were reported for rate constant

measurements at metal electrodes.48, 49 Compound VIII had a reorganization energy (λ) of 1.5 eV,50-53 which according to Eq. 2.5 results in a k_et,max of 2×10-17 cm4 s-1, which is in accordance with theoretical predictions.37 Trisbipyridinecobalt(III/II) on the other hand is a very well-studied one-electron transition metal complex, for which the above stated complications do not exist. Hence this compound is particularly suited for mechanistic studies of k_et. The rate constant for electron transfer for this contact was found to be extremely small, k_et = (2 ± 0.4) ×10-25 cm4 s-1. The reorganization energy of compound VI is approximately 2.3 eV,24 which is very high in comparison with the λ of Os-

a _{electrode used as received}

b _{same electrode as in} a_{; electrode was repolished} c _{same electrode as in} a_{; re-etched}

d _{same electrode as in} a_{; repolished} Experiments γ [-] E shift

[mV] 10

-17 _N

D [cm-3]

∆Go’ [eV] ket [cm4/sec]

ZnO3_VIII_ph8.7 a 70/7 mM ([A]/[A]-) 1.13 60 (61) 0.8 0.600±0.014 _{(1.1±0.6)×10}-21 7/7 mM (([A]/[A]-) 1.10 ZnO3_VIII_pH8.7a b 70/7 mM ([A]/[A]-) 1.10 60 (61) 0.79 0.510±0.012 _(5±2)×10-23 7/7 mM ([A]/[A]-) 1.11 70(64) 0.7/7 mM ([A]/[A]-) 1.14 ZnO3_VII_pH7.0 c 7/1 mM ([A]/[A]-) 1.05 0 (34) 0.9 0.350±0.012 N/A 3.16/1 mM ([A]/[A]-) 1.10 ZnO3_VI_pH8.7 d 10/1 mM ([A]/[A]-) 1.08 62 (61) 0.78 0.310±0.010 _{(2.0±0.4)×10}-25 1/1 mM ([A]/[A]-) 1.07

TABLE 2.5. Results of rate constant measurements involving electrode ZnO3 and redox compounds VI, VII, VIII.

agreement of k_et,max = 4×10-18 cm4 s-1 with the theoretical prediction especially in direct comparison with [Fe(CN)₆]3-/4-, is satisfactory and gives a first indication for a

pronounced reorganization energy dependence of k_et.

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