trilayer_stacked : Momentum-space Continuum Calculation of DOS and MHC-DOS Kinetic Rates in Stacked Trilayer Graphene

Calculation density of states for ABA/ABC stacked trilayer graphene using a low-energy momentum space model (or Fourier transformed tight-binding model). The DOS files are used as input to the MHC-DOS model for charge transfer rates with redox couple (Ruthenium Hexamine). For rate model see the Julia-based ElectrochemicalKinetics.jl package.

Contact

Dr. Stephen Carr : stephen_carr1@brown.edu

Mohammad Babar : mdbabar@umich.edu

Code descriptions

Main file descriptions are as follows, other files are either output or supporting function files.

1. trilayer_stacking_band_calc.m generates DOS files for ABA or ABC stacking using tight binding. named ABC_dos.mat or ABA_dos.mat. Description of input arguments can be found at the beginning of the file.

2. script.jl main Julia calculation script that outputs .mat file with oxidation (k_ox) and reduction rates (k_red) for specified parameters $A$ , $\lambda$ and $\eta$.

where $\lambda$ = reorganization energy (eV), $\eta$ = applied overpotential (V) and $A$ = proportionality constant for MHC-DOS theory. Other input parameters:

i. C_dl : EDL capacitance (F)

ii. V_dl : EDL voltage (V)

iii. C_q : Quantum capacitance (F)

iv. V_q : Quantum capacitance voltage (V)

v. Vq_min / Vq_max : Min/Max range of Quantum capacitance voltage for interpolation (Eq. 3 in paper)

vi. kT : Thermal energy to temperature setting (0.26 eV at 300 K)

vii. ef : Fermi energy of the electrode

Run Julia scripts using:

> julia script.jl

The output prints the rates, e.g. for Ruthenium Hexamine (default parameters in script.jl)

ABA k_ox 2.6323040539732973e-5 k_red 2.6323040539732787e-5
ABC k_ox 2.77951068679322e-5 k_red 2.7795106867932337e-5

Here LHS and RHS rates are equal as η = 0.0 (no driving force).