spcal.particle

Functions for particle calculations.

spcal.particle.atoms_per_particle(masses: float | ndarray, molar_mass: float) → float | ndarray

Number of atoms per particle.

\(N = \frac{m (kg) N_A ({mol}^{-1})}{M ({kg} \cdot {mol}^{-1})}\)

Parameters:

• masses – array of particle masses (kg)

• molar_mass – molecular weight (kg/mol)

spcal.particle.cell_concentration(masses: float | ndarray, diameter: float, molar_mass: float) → float | ndarray

Calculates intracellular concentrations.

\(c (mol \cdot L^{-1}) = \frac{6 m (kg)}{ 4 \pi d (m)^3 M ({kg} \cdot {mol}^{-1}) 1000 (L \cdot m^3)}\)

Parameters:

• masses – array of material masses (kg)

• diameter – cell diameter (m)

• molar_mass – molecular weight (kg/mol)

spcal.particle.nebulisation_efficiency_from_mass(signal: float | ndarray, dwell: float, mass: float, flow_rate: float, response_factor: float, mass_fraction: float = 1.0) → float

Calculates efficiency for signals given a defined mass.

\(\eta = \frac{m (kg) s (L \cdot {kg}^{-1}) f} {I V (L \cdot {s}^{-1}) t (s)}\)

Parameters:

• signal – array of reference particle signals

• dwell – dwell time (s)

• mass – of reference particle (kg)

• flow_rate – sample inlet flowrate (L/s)

• response_factor – counts / concentration (kg/L)

• mass_fraction – molar mass analyte / molar mass particle

spcal.particle.nebulisation_efficiency_from_mass_concentration(count: int, mass_concentration: float, mass: float, flow_rate: float, time: float) → float

The nebulistaion efficiency given a defined concentration. “This is the number concentration calculated using the mass of the particles.”

\(\eta = \frac{m (kg) N}{c ({kg} \cdot L^{-1}) V (L \cdot s^{-1}) t (s)}\)

Parameters:

• count – number of detected particles

• mass_concentration – of reference material (kg/L)

• mass – of reference material (kg)

• flow_rate – sample inlet flow (L/s)

• time – total aquisition time (s)

spcal.particle.nebulisation_efficiency_from_number_concentration(count: int, number_concentration: float, flow_rate: float, time: float) → float

The nebulistaion efficiency given a number concentration.

\(\eta = \frac{N}{c ({#} \cdot L^{-1}) V (L \cdot s^{-1}) t (s)}\)

Parameters:

• count – number of detected particles

• number_concentration – of reference material (#/L)

• flow_rate – sample inlet flow (L/s)

• time – total aquisition time (s)

spcal.particle.particle_mass(signal: float | ndarray, dwell: float, efficiency: float, flow_rate: float, response_factor: float, mass_fraction: float = 1.0) → float | ndarray

Array of particle masses given their integrated responses.

\(m (kg) = \frac{\eta t (s) I V (L \cdot s^{-1})} {s (L \cdot {kg}^{-1}) f}\)

Parameters:

• signal – array of particle signals

• dwell – dwell time (s)

• efficiency – nebulisation efficiency

• flow_rate – sample inlet flowrate (L/s)

• response_factor – counts / concentration (kg/L)

• mass_fraction – molar mass analyte / molar mass particle

spcal.particle.particle_number_concentration(count: int, efficiency: float, flow_rate: float, time: float) → float

Number concentration.

\({PNC} (L^{-1}) = \frac{N}{\eta V (L \cdot s^{-1}) T (s)}\)

Parameters:

• count – number of detected particles

• efficiency – nebulisation efficiency

• flow_rate – sample inlet flowrate (L/s)

• time – total aquisition time (s)

spcal.particle.particle_size(masses: float | ndarray, density: float) → float | ndarray

Array of particle diameters.

\(d (m) = \sqrt[3]{\frac{6 m (kg)}{\pi \rho ({kg} \cdot m^3)}}\)

Parameters:

• masses – array of particle signals (kg)

• density – reference density (kg/m3)

spcal.particle.particle_total_concentration(masses: float | ndarray, efficiency: float, flow_rate: float, time: float) → float

Concentration of material.

\(C (kg L^{-1}) = \sum{\frac{m (kg)}{\eta V (L \cdot s^{-1}) T (s)}}\)

Parameters:

• masses – array of particle signals (kg)

• efficiency – nebulisation efficiency

• flow_rate – sample inlet flowrate (L/s)

• time – total aquisition time (s)

spcal.particle.reference_particle_mass(density: float, diameter: float) → float

Calculates particle mass assusming a spherical particle.

\(m (kg) = \frac{4}{3} \pi (\frac{d (m)}{2})^3 \rho ({kg} \cdot m^3)\)

Parameters:

• density – reference density (kg/m3)

• diameter – reference diameter (m)