ET of Au MPCs freely diffusing in solution

ET in solutions- either in aqueous or organic media- is typically studied as an electron exchange between a freely diffusing Au MPC and an electrode surface. Little is known about the exact details of the interaction between MPC and electrode surface, but in an oxidation reaction, the electron is hypothesized to be transferred from within the metal core of the cluster, tunneling through the insulating ligand to the electrode surface. In a reduction reaction, the reverse process occurs.

ET in solutions of Au MPCs are typically studied by cyclic voltammetry or scanning electrochemical microscopy (SECM). A report from the Cliffel group78 _{established a}

methodology for measuring the forward heterogeneous ET rate through the thiol monolayer of Au MPCs in solution, using the SECM feedback mode. They develop a formula for extracting the ET rate constant from SECM approach curves for monodisperse thiolate-protected Au144

MPCs. They found that in freely diffusing solution, the MPC ligand length tends to be the more dominant factor in determining the rate constant of ET; a C6 ligand gave an ET rate constant

(0.11 cm/s) two orders of magnitude larger than C12 (0.0048 cm/s). For phenylethanethiol-

protected Au144, the rate of ET was 0.035 cm/s, on the same order of magnitude as C8 (0.024

cm/s) and one order slower than C6, showingthat ligand aromaticity is not a significant player in

ET kinetics in solution. In comparing ET kinetics amongst different clusters with respect to core size, the ET rate constants for hexanethiolate-protected Au25 clusters were determined by cyclic

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of magnitude lower than the ET rate constant for hexanethiolate-protected Au144. Looking at

differences in ET kinetics amongst redox couples of the same cluster, Maran, et al.58 measured the rate in ET in hexanethiolate-protected Au25 clusters via CV and found that ET rates for the

+1/0 charge state transition were slower than those of the 0/-1 redox couple, by about one-half an order of magnitude. The above results indicate that the effects on ET rate in order of most to least influential are: ligand length, core size, and redox couple.

ET kinetics have also been characterized in Au MPC molecular melts. Electron transport through the undiluted room temperature melt occurs by a diffusion-like core-to-core electron hopping process. In a molecular melt of polyethylene glycol (PEG)-protected Au25 MPCs, first

order electron hopping rate constant of 2 × 104 _s-1 _{and second order rate constant of 3.8 × 10}5 _M-1

s-1 were obtained via potential step chronoamperometry.80 In a later report, addition of electrolyte and free PEG or CO2 as plasticizers to a molecular melt of polyethylene glycol-

protected Au25 MPCs resulted in the formation of a conductive room temperature molten salt.

Activation energies of transport and rates of both electron and counterion transport within the melt were measured using voltammetry, chronoamperometry, and electrochemical impedance. Rates and activation energies were found to correlate closely with each other. Plasticization by addition of small molecule solvent components resulted in a four-fold increase in kEX (from 1.15

to 4.4 x 10-7 M-1 s-1) and halving of EA (from 50 to 22 kJ mol-1).54

As an aside, note that different units are used for the homogeneous and heterogeneous ET rate constants. It is in fact not straightforward to compare these rate constants obtained through different methods and conversions between units can be approximate. Different theories can model the ET transfer as an electron diffusion coefficient (DE, cm2 s-1), a first order reaction

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(kHOP, s-1), or a second order (kEX, M-1 s-1) process. This produces the diversity of units found in

the literature for electron transport in MPCs. Their equivalences are80

𝐷𝐸 =𝑘𝐻𝑂𝑃𝛿

2

6 =

𝑘𝐸𝑋𝛿2𝐶

6 (1.4)

Calculating the ET rate constant in different ways is sometimes helpful for comparison of values across the literature. Sometimes, a more general kET is used.

It was also discovered that ET between Au MPCs in solution can be manipulated, due to electron parity of the cluster, by an applied external magnetic field. This topic is called

magnetoelectrochemistry. External magnetic fields can influence ET kinetics by changing the field-induced splitting of originally degenerate energy states. Redox potentials of Au MPCs and subsequent currents become dependent on electrode orientation within the magnetic field and magnetic field strength.81,82

ETs in solutions of Au MPCs can also be described in terms of their exchanges with an additional redox species in solution. Murray, et al.83 showed that MPCs could undergo ET reactions with other redox-active species in their solutions. In later experiments by Kontturi et al.,84 ET reaction between organic-soluble Au MPCs and an aqueous redox species (Ce(IV), Fe(CN)63-/4-, Ru(NH3)63+, and Ru(CN)64-) was measured with both feedback and potentiometric

modes of SECM. Charge transfers occurring heterogeneously at the liquid-liquid interface were slow compared to electron self-exchanges between MPCs. In a report by Murray, et al.,22 the bimolecular rate constant of the reaction between organic-soluble Au25 clusters (mislabeled as

Au38) and an aqueous redox species was determined through negative-feedback SECM approach

curves. In agreement with predictions from Marcus theory, this process involving Au MPCs at the liquid-liquid interface was faster than ET reactions between conventional aqueous and organic redox species.

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