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Pt Oxigen Reduction Reaction

pySNOW contains tools to estimate ORR electrocatalytic activity for Pt nanoparticles as in:

Rossi, K.; Asara, G. G.; Baletto, F. "A genomic characterisation of monometallic nanoparticles". Phys. Chem. Chem. Phys. 2019, 21, 4888–4898. DOI: https://doi.org/10.1039/C8CP05720F

The module provides routines to compute geometrical descriptors, surface properties, and electrochemical activity metrics (specific activity, mass activity, and overpotential) from atomistic nanoparticle structures.

The use cases are documented in the correpsonding tutorial.

snow.catalysis.Pt_ORR

get_geometry_properties(coords)

Compute basic geometrical properties of the nanoparticle.

Parameters:

Name Type Description Default
coords ndarray of shape (N, 3)

Cartesian coordinates of the atoms in Angstrom.

 required

Returns:

Type Description
dict

Dictionary containing:

  • natoms : int Total number of atoms.
  • rij_max : float Maximum interatomic distance in Angstrom.
Source code in snow/catalysis/Pt_ORR.py 
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def get_geometry_properties(coords):
    """
    Compute basic geometrical properties of the nanoparticle.

    Parameters
    ----------
    coords : ndarray of shape (N, 3)
        Cartesian coordinates of the atoms in Angstrom.

    Returns
    -------
    dict
        Dictionary containing:

        - ``natoms`` : int
            Total number of atoms.
        - ``rij_max`` : float
            Maximum interatomic distance in Angstrom.
    """

    natoms = len(coords)
    rij_max = np.max(pdist(coords))
    return {"natoms": natoms, "rij_max": rij_max}

get_physical_and_surface_props(agcns, num_nn, natoms, lattice, mass_pt_mg=None)

Compute physical and surface-related properties of a Pt nanoparticle.

Parameters:

Name Type Description Default
agcns ndarray

Array of generalized coordination numbers (GCN/AGCN) for each atom.

 required
num_nn ndarray

Number of nearest neighbours for each atom.

 required
natoms int

Total number of atoms in the nanoparticle.

 required
lattice float

FCC lattice parameter in Angstrom.

 required
mass_pt_mg float

Mass of a single Pt atom in milligrams. If not provided, the value is computed from the atomic mass of Pt.

 None

Returns:

Type Description
dict

Dictionary containing:

  • mass_np_mg : float Total nanoparticle mass in milligrams.
  • active_surf_m2 : float Electrochemically active surface area in m².
  • active_surf_cm2 : float Electrochemically active surface area in cm².
  • counter_surf : int Number of surface atoms.
  • surf_mask : ndarray of bool Boolean mask identifying surface atoms (atoms with coordination number < 11).
Notes

Surface atoms are identified using a nearest-neighbour criterion (coordination number < 11).

Source code in snow/catalysis/Pt_ORR.py 
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def get_physical_and_surface_props(agcns, num_nn, natoms, lattice, mass_pt_mg=None):
    """
    Compute physical and surface-related properties of a Pt nanoparticle.

    Parameters
    ----------
    agcns : ndarray
        Array of generalized coordination numbers (GCN/AGCN)
        for each atom.

    num_nn : ndarray
        Number of nearest neighbours for each atom.

    natoms : int
        Total number of atoms in the nanoparticle.

    lattice : float
        FCC lattice parameter in Angstrom.

    mass_pt_mg : float, optional
        Mass of a single Pt atom in milligrams.
        If not provided, the value is computed from the
        atomic mass of Pt.

    Returns
    -------
    dict
        Dictionary containing:

        - ``mass_np_mg`` : float
            Total nanoparticle mass in milligrams.
        - ``active_surf_m2`` : float
            Electrochemically active surface area in m².
        - ``active_surf_cm2`` : float
            Electrochemically active surface area in cm².
        - ``counter_surf`` : int
            Number of surface atoms.
        - ``surf_mask`` : ndarray of bool
            Boolean mask identifying surface atoms
            (atoms with coordination number < 11).

    Notes
    -----
    Surface atoms are identified using a nearest-neighbour
    criterion (coordination number < 11).
    """

    atomic_r_AA = lattice/(2 * np.sqrt(2))
    atomic_r_m=atomic_r_AA* 1e-10

    print(atomic_r_m)
    if mass_pt_mg is not None:
        mass_Pt_mg=mass_pt_mg
    else:
        mass_Pt_amu=mass["Pt"]
        mass_Pt_mg = mass_Pt_amu * 1.66053906660e-21

    print(mass_Pt_mg)
    mass_np_mg = mass_Pt_mg * natoms
    surf_mask = (num_nn < 11)
    counter_surf = np.sum(surf_mask)

    # Area Attiva (m^2)
    active_surf_m2 = np.sum(4 * np.pi * (atomic_r_m**2) * ((12.0 - agcns[surf_mask]) / 12.0))

    return {
        "mass_np_mg": mass_np_mg,
        "active_surf_m2": active_surf_m2,
        "active_surf_cm2": active_surf_m2 * 1e4,
        "counter_surf": counter_surf,
        "surf_mask": surf_mask
    }

calculate_volcano_dg_fortran(gcn_unique)

Compute adsorption free-energy corrections from the volcano relationship as in

Parameters:

Name Type Description Default
gcn_unique ndarray

Array of unique generalized coordination numbers.

 required

Returns:

Type Description
ndarray

Free-energy descriptor values (eV) associated with each GCN value.
Source code in snow/catalysis/Pt_ORR.py 
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def calculate_volcano_dg_fortran(gcn_unique):
    """
    Compute adsorption free-energy corrections from the
    volcano relationship as in 

    Parameters
    ----------
    gcn_unique : ndarray
        Array of unique generalized coordination numbers.

    Returns
    -------
    ndarray
        Free-energy descriptor values (eV) associated
        with each GCN value.
    """


    return np.where(gcn_unique < 8.33,
                    0.192 * (gcn_unique) - 0.724,
                    -0.178 * (gcn_unique) + 2.345)

perform_activity_analysis(unique_gcns, occurrences, phys_props)

Compute electrochemical activity metrics for a Pt nanoparticle.

Parameters:

Name Type Description Default
unique_gcns ndarray

Unique generalized coordination number values.

 required
occurrences ndarray

Number of occurrences associated with each GCN value.

 required
phys_props dict

Dictionary containing physical and surface properties returned by get_physical_and_surface_props.

 required

Returns:

Name Type Description
sa_09 float

Specific activity at 0.9 V.
ma_09 float

Mass activity at 0.9 V in mA/mg.
eta1 float

Overpotential corresponding to a total current density larger than 1 mA/cm².
Source code in snow/catalysis/Pt_ORR.py 
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def perform_activity_analysis(unique_gcns, occurrences, phys_props):
    """
    Compute electrochemical activity metrics for a Pt nanoparticle.

    Parameters
    ----------
    unique_gcns : ndarray
        Unique generalized coordination number values.

    occurrences : ndarray
        Number of occurrences associated with each GCN value.

    phys_props : dict
        Dictionary containing physical and surface properties
        returned by ``get_physical_and_surface_props``.

    Returns
    -------
    sa_09 : float
        Specific activity at 0.9 V.

    ma_09 : float
        Mass activity at 0.9 V in mA/mg.

    eta1 : float
        Overpotential corresponding to a total current density
        larger than 1 mA/cm².

    """

    u_bins = np.arange(1, 1299) * 0.001 # j*0.001
    total_current = np.zeros_like(u_bins)

    dg_values = calculate_volcano_dg_fortran(unique_gcns)

    freq = occurrences / np.sum(occurrences)

    for j_idx, u in enumerate(u_bins):

        delta = (dg_values - u) / KB_T
        j_lim = unique_gcns * 12.65 #mA cm^-2

        site_currents = np.exp(delta) * freq * j_lim
        total_current[j_idx] = np.sum(site_currents)

    # SA a 0.9V (index is 899 because u = 900 * 0.001)
    sa_09 = total_current[899]

    # Change the bin if you want change the applied potential SA a 0.88V (index is 879 because u = 880 * 0.001)
    #sa_09 = total_current[879]

    ma_09 = sa_09 * (phys_props['active_surf_cm2']) / phys_props['mass_np_mg']

    eta1 = 0.0
    for j_idx in range(len(u_bins)-1, -1, -1):
        if total_current[j_idx] > 1.0:
            eta1 = V_REVERSIBLE - u_bins[j_idx]
            break

    return sa_09, ma_09, eta1