Python Access

mpbpsolve(; n=21, 
            chargenumbers=[-1, 1], 
            domain=[0, 1.0e-10], 
            surfacecharge=[0.16, -0.16], 
            bulkmolarity=0.1)

Solve the modified Poisson-Boltzmann problem with specified bulk molarity.

This function solves the modified Poisson-Boltzmann equation for a 1D domain with specified surface charges and bulk ion concentrations. The solver uses a finite volume method with ExtendableGrids and VoronoiFVM.

Arguments

• n::Int=21: Number of grid points along the domain. Default is 21.
• chargenumbers::Vector{Int}=[-1, 1]: Charge numbers of the ionic species (e.g., [-1, 1] for monovalent anions and cations).
• domain::Vector{Float64}=[0, 1.0e-10]: Domain boundaries in meters [start, end]. Default is [0, 1.0e-10] (0 to 0.1 nm).
• surfacecharge::Vector{Float64}=[0.16, -0.16]: Surface charge densities at the domain boundaries in C/m².
• bulkmolarity::Float64=0.1: Bulk molarity of the electrolyte solution in mol/L.

Returns

• X: Grid coordinates in m (Vector{Float64})
• c0: Solvent concentration in mol/L (Vector{Float64})
• c1: Concentration of first ionic species along the grid in mol/L (Vector{Float64})
• c2: Concentration of second ionic species along the grid in mol/L(Vector{Float64})

Examples

# Solve with default parameters
X, c0, c_anion, c_cation = mpbpsolve()

# Solve with custom parameters
X, c0, c_anion, c_cation = mpbpsolve(
    n=51,
    chargenumbers=[-1, 1],
    domain=[0, 2.0e-10],
    surfacecharge=[0.2, -0.2],
    bulkmolarity=0.15
)

Notes

• The function automatically creates a uniform grid over the specified domain
• A boundary face mask is applied at the domain midpoint in order fix the pressure value there
• The solver uses damped Newton iteration with initial damping factor of 0.05
• Surface charges should be specified in SI units (C/m²)
• Domain should be specified in SI units (meters)

icmpbpsolve(; n=21, 
              chargenumbers=[-1, 1], 
              domain=[0, 1.0e-10], 
              surfacecharge=[0.16, -0.16], 
              averagemolarity=1)

Solve the ion-conserving modified Poisson-Boltzmann problem with specified average molarity.

This function solves the modified Poisson-Boltzmann equation with ion conservation constraints. Unlike mpbpsolve, this solver conserves the total number of ions in the system and uses an average molarity parameter rather than bulk molarity. This is particularly useful for systems where ion conservation is physically important.

Arguments

• n::Int=21: Number of grid points along the domain. Must be odd (automatically incremented if even). Default is 21.
• chargenumbers::Vector{Int}=[-1, 1]: Charge numbers of the ionic species (e.g., [-1, 1] for monovalent anions and cations).
• domain::Vector{Float64}=[0, 1.0e-10]: Domain boundaries in meters [start, end]. Default is [0, 1.0e-10] (0 to 0.1 nm).
• surfacecharge::Vector{Float64}=[0.16, -0.16]: Surface charge densities at the domain boundaries in C/m².
• averagemolarity::Float64=1: Average molarity of the electrolyte solution in mol/L.

Returns

• X: Grid coordinates in m (Vector{Float64})
• c0: Solvent concentration in mol/L (Vector{Float64})
• c1: Concentration of first ionic species along the grid in mol/L (Vector{Float64})
• c2: Concentration of second ionic species along the grid in mol/L (Vector{Float64})

Examples

# Solve with default parameters
X, c0, c_anion, c_cation = icmpbpsolve()

# Solve with custom parameters and higher resolution
X, c0, c_anion, c_cation = icmpbpsolve(
    n=101,
    chargenumbers=[-2, 1],  # divalent anions, monovalent cations
    domain=[0, 5.0e-10],
    surfacecharge=[0.3, -0.3],
    averagemolarity=0.5
)

Notes

• The function enforces an odd number of grid points for numerical stability
• Ion conservation is enforced through the conserveions=true parameter in AugmentedPBData
• The solver employs damped Newton iteration with initial damping factor of 0.05
• Average molarity represents the spatial average concentration, which may differ from bulk concentration due to ion conservation
• Surface charges should be specified in SI units (C/m²)
• Domain should be specified in SI units (meters)

Differences from mpbpsolve

• Enforces ion conservation constraints
• Uses average rather than bulk molarity
• Requires odd number of grid points
• May show different concentration profiles due to conservation effects

prepare_grid(n, domain)

Prepare eqidistant simulation grid. Add interface region in the mid of the domain in order to fix pressure and provide location for ion conservation constraints.