Horowitz-Metzger Method

horowitz_metzger_method(temperature: np.ndarray, alpha: np.ndarray, n: float = 1) → Tuple[float, float, float, float]

Perform Horowitz-Metzger analysis to determine kinetic parameters for thermal decomposition reactions.

Parameters:

  • temperature (np.ndarray) – Temperature data in Kelvin.

  • alpha (np.ndarray) – Conversion data.

  • n (float) – Reaction order. Default is 1.

Returns:

Tuple containing activation energy (E_a in J/mol), pre-exponential factor (A in min^-1), temperature of maximum decomposition rate (T_s in K), and R-squared value.

Return type:

Tuple[float, float, float, float]

Theory

The Horowitz-Metzger method is used for determining kinetic parameters from thermogravimetric data. It is based on the following equation:

\[\ln[-\ln(1-\alpha)] = \frac{E_a\theta}{RT_s^2}\]
where:

  • α is the conversion

  • E_a is the activation energy

  • θ is T - T_s

  • T_s is the temperature at the maximum rate of decomposition

  • R is the gas constant

Usage Example

import numpy as np
from pkynetics.model_fitting_methods import horowitz_metzger_method
from pkynetics.result_visualization import plot_horowitz_metzger

# Generate sample data
temperature = np.linspace(300, 800, 1000)
alpha = 1 - np.exp(-0.01 * (temperature - 300))

# Perform Horowitz-Metzger analysis
e_a, a, t_s, r_squared = horowitz_metzger_method(temperature, alpha)

print(f"Activation energy (E_a): {e_a/1000:.2f} kJ/mol")
print(f"Pre-exponential factor (A): {a:.2e} min^-1")
print(f"Temperature of max decomposition rate (T_s): {t_s:.2f} K")
print(f"R-squared: {r_squared:.4f}")

# Visualize results (assuming a plot_horowitz_metzger function exists)
plot_horowitz_metzger(temperature, alpha, e_a, a, t_s, r_squared)

Parameters

  • temperature (np.ndarray): Temperature data in Kelvin. Must be in ascending order.

  • alpha (np.ndarray): Conversion data. Must be between 0 and 1 (exclusive).

  • n (float, optional): Reaction order. Default is 1.

Returns

A tuple containing:

  1. e_a (float): Activation energy in J/mol.

  2. a (float): Pre-exponential factor in min^-1.

  3. t_s (float): Temperature of maximum decomposition rate in K.

  4. r_squared (float): Coefficient of determination (R^2) of the fit.

Raises

  • ValueError: If input arrays have different lengths or contain invalid values.

Notes

  • The method uses smoothed derivative data to determine the temperature of maximum decomposition rate (T_s).

  • The analysis focuses on the most linear region of the data, typically between 20-80% conversion.

  • If not enough points are available in the 20-80% conversion range, the range is expanded to 10-90%.

  • The method assumes first-order kinetics by default, but other reaction orders can be specified.

See Also