Diffusional Electron Transport Coupled to Thermodynamically Driven Electron Transfers in Redox-Conductive Multivariate Metal–Organic Frameworks

The development of redox-conductive metal–organic frameworks (MOFs) and the fundamental understanding of charge propagation through these materials are central to their applications in energy storage, electronics, and catalysis. To answer some unresolved questions about diffusional electron hopping transport and redox conductivity, mixed-linker MOFs were constructed from two statistically distributed redox-active linkers, pyromellitic diimide bis-pyrazolate (PMDI) and naphthalene diimide bis-pyrazolate (NDI), and grown as crystalline thin films on conductive fluorine-doped tin oxide (FTO). Owing to the distinct redox properties of the linkers, four well-separated and reversible redox events are resolved by cyclic voltammetry, and the mixed-linker MOFs can exist in five discrete redox states. Each state is characterized by a unique spectroscopic signature, and the interconversions between the states can be followed spectroscopically under operando conditions. With the help of pulsed step-potential spectrochronoamperometry, two modes of electron propagation through the mixed-linker MOF are identified: diffusional electron hopping transport between linkers of the same type and a second channel that arises from thermodynamically driven electron transfers between linkers of different types. Corresponding to the four redox events of the mixed-linker MOFs, four distinct bell-shaped redox conductivity profiles are observed at a steady state. The magnitude of the maximum redox conductivity is evidenced to be dependent on the distance between redox hopping sites, analogous to the situation for apparent electron diffusion coefficients, Deapp, that are obtained in transient experiments. The design of mixed-linker redox-conductive MOFs and detailed studies of their charge transport properties present new opportunities for future applications of MOFs, in particular, within electrocatalysis.


Figure S35
. Spectrochronoamperometry monitoring the evolution of NDI •− (471 nm), NDI 2-(418 nm), PMDI •− (713 nm), and PMDI 2-(551 nm) after holding the potential at -1.9 V vs Ag/AgNO3 for 50 s then followed by open circuit operation to let the system to relax.In the presence of trace amount of atmospheric oxygen molecules, the reduced species will be gradually re-oxidized to neutral state.

Equivalent circuits
Figure S1. 1 HNMR of NDI linker measured in DMSO-d6 at 293 K.The nondeuterated solvent and water are marked with asterisk sign.

Figure
Figure S2. 1 H NMR spectrum of PMDI in DMSO-d6 at 293 K. Peak at 3.33 ppm corresponds to water, 5.63 ppm corresponds to DCM.

Figure S4 .
Figure S4.UV-vis absorption spectra of the free PMDI linker in DMF, showing that the electronic π−π* transitions in the neutral states.UV-vis absorption of PMDI in solution is measured with DMF as reference to avoid any possible contribution from DMF.

Figure S5 .
Figure S5.CV of NDI linkers measured at scan rates from 50 mV s -1 in DMF with 0.1 M KPF6 as the supporting electrolyte.

Figure S6 .
Figure S6.CV of PMDI linkers measured at scan rates from 50 mV s -1 in DMF with 0.1 M KPF6 as the supporting electrolyte.

Figure S10 .
Figure S10.Thin film CV of mixed linker Zn(NDI)0.8(PMDI)0.2on FTO surface with a scan rate of 10 mV s -1 .The integrated area was used to determine the ratio of NDI to PMDI in the mixed linker MOFs.All electrochemistry data were collected in Ar-saturated DMF with KPF6 as the supporting electrolyte (0.1 M).

Figure S11 .
Figure S11.Thin film CV of mixed linker Zn(NDI)0.5(PMDI)0.5 on FTO surface with a scan rate of 10 mV s -1 .The integrated area was used to determine the ratio of NDI to PMDI in the mixed linker MOFs.All electrochemistry data were collected in Ar-saturated DMF with KPF6 as the supporting electrolyte (0.1 M).

Figure S12 .
Figure S12.Thin film CV of mixed linker Zn(NDI)0.2(PMDI)0.8on FTO surface with a scan rate of 10 mV s -1 .The integrated area was used to determine the ratio of NDI to PMDI in the mixed linker MOFs.All electrochemistry data were collected in Ar-saturated DMF with KPF6 as the supporting electrolyte (0.1 M).

Figure S14 .
Figure S14.UV-vis absorption spectra of the mono-linker Zn(NDI) thin film on FTO measured in DMF, showing that the electronic π−π* transitions in the neutral states.UV-vis absorption was measured with bare FTO in DMF as reference to avoid any possible contribution from both the electrode and solvent.

Figure S16 .
Figure S16.UV-vis spectroelectrochemistry measurements of the Zn(NDI) thin film while slowing reducing it with finely modulated applied potential to access the vibrational signature of different redox states, singly reduced radical state Zn(NDI •− ) (a) and doubly reduced dianion state Zn(NDI 2− ) (b).

Figure S17 .
Figure S17.UV-vis spectroelectrochemistry measurements of the Zn(NDI) thin film while slowing reoxidizing it with finely modulated applied potential to access the vibrational signature of different redox states, from doubly reduced dianion state Zn(NDI 2− ) to singly reduced radical state Zn(NDI •− ) (a), and further to neutral Zn(NDI) state (b).

Figure S18 .
Figure S18.UV-vis spectroelectrochemistry measurements of the Zn(PMDI) thin film while slowing reducing it with finely modulated applied potential to access the vibrational signature of different redox states, singly reduced radical state Zn(PMDI •− ) (a) and doubly reduced dianion state Zn(PMDI 2− ) (b).

Figure S19 .
Figure S19.UV-vis spectroelectrochemistry measurements of the Zn(PMDI) thin film while slowing reoxidizing it with finely modulated applied potential to access the vibrational signature of different redox states, from doubly reduced dianion state Zn(PMDI 2− ) to singly reduced radical state Zn(PMDI •− ) (a), and further to neutral Zn(PMDI) state (b).

Figure S27 .
Figure S27.Pulsed step-potential spectrochronoamperometry monitoring the evolution of NDI 2-(418 nm)after stepping the potential from -0.2 V to -1.9 V vs Ag/AgNO3 followed by open circuit operation, the pulse was prolonged from 1 to 40 s.

Figure S28 .
Figure S28.Pulsed step-potential spectrochronoamperometry monitoring the evolution of PMDI •− (713nm) after stepping the potential from -0.2 V to -1.9 V vs Ag/AgNO 3 followed by open circuit operation, the pulse was prolonged from 1 to 40 s.

Figure S29 .
Figure S29.Pulsed step-potential spectrochronoamperometry monitoring the evolution of PMDI 2-(551nm) after stepping the potential from -0.2 V to -1.9 V vs Ag/AgNO3 followed by open circuit operation, the pulse was prolonged from 1 to 40 s.

Figure S32 .
Figure S32.Spectrochronoamperometry monitoring the evolution of NDI •− (471 nm), NDI 2-(418 nm), PMDI •− (713 nm), and PMDI 2-(551 nm) after holding the potential at -1.1 V vs Ag/AgNO3 for 50 s thenfollowed by open circuit operation to let the system to relax.In the presence of trace amount of atmospheric oxygen molecules, the reduced species will be gradually re-oxidized to neutral state.

Figure S33 .
Figure S33.Spectrochronoamperometry monitoring the evolution of NDI •− (471 nm), NDI 2-(418 nm), PMDI •− (713 nm), and PMDI 2-(551 nm) after holding the potential at -1.3 V vs Ag/AgNO3 for 50 s thenfollowed by open circuit operation to let the system to relax.In the presence of trace amount of atmospheric oxygen molecules, the reduced species will be gradually re-oxidized to neutral state.

Figure S36
Figure S36 Equivalent circuits (EC) for simulation of the experimental impedance date.(a) Simplified RC circuit, where Rct and Cct stand for resistance and capacitance related to the inter-site cation coupled electron hopping.(b) Modified RC circuit by adding the serial a constant phase element (CPE) to the electronic resistance component, where CPE is primarily defined by its phase, n (0 ≤ n ≤ 1), when n equals 1, 0.5, or 0, the CPE represent an ideal capacitor, a semi-infinite diffusional Warburg element, and an ideal resistor, respectively.(c) Modified RC circuit by adding the serial Warburg element to the electronic resistance component.In all circuits, Rs stands for the resistance related to electrolyte.

Figure S38 .
Figure S38.Evolution of redox conductivity (upper panel, simulated from Fig. S36a), Warburg coefficient (middle panel, simulated from Fig. S36c) and CPE coefficient (lower panel, simulated from Fig. S36b) as the function of electrochemical potential (of the thin-film) measured in 0.1 M KPF6 DMF electrolyte, which is determined by the redox state of the Zn(NDI)0.2(PMDI)0.8thin film.Note that the unit of the Y-axes for lower panel depends upon the phase, n; to facilitate comparison, n was assumed to be 0.5 here.Gaussian fit was performed for the NDI/NDI •− based, PMDI/PMDI •− based, NDI •− /NDI 2− based and PMDI •− /PMDI 2− based bell-shaped redox conductivities.

Figure S39 .
Figure S39.Evolution of redox conductivity (upper panel, simulated from Fig. S36a), Warburg coefficient (middle panel, simulated from Fig. S36c) and CPE coefficient (lower panel, simulated from Fig. S36b) as the function of electrochemical potential (of the thin-film) measured in 0.1 M KPF6 DMF electrolyte, which is determined by the redox state of the Zn(NDI)0.5(PMDI)0.5thin film.Note that the unit of the Y-axes for lower panel depends upon the phase, n; to facilitate comparison, n was assumed to be 0.5 here.Gaussian fit was performed for the NDI/NDI •− based, PMDI/PMDI •− based, NDI •− /NDI 2− based and PMDI •− /PMDI 2− based bell-shaped redox conductivities.

Figure S40 .
Figure S40.Evolution of redox conductivity (upper panel, simulated from Fig. S36a), Warburg coefficient (middle panel, simulated from Fig. S36c) and CPE coefficient (lower panel, simulated from Fig. S36b) as the function of electrochemical potential (of the thin-film) measured in 0.1 M KPF6 DMF electrolyte, which is determined by the redox state of the Zn(NDI)0.8(PMDI)0.2thin film.Note that the unit of the Y-axes for lower panel depends upon the phase, n; to facilitate comparison, n was assumed to be 0.5 here.Gaussian fit was performed for the NDI/NDI •− based, PMDI/PMDI •− based, NDI •− /NDI 2− based and PMDI •− /PMDI 2− based bell-shaped redox conductivities.