Lauritzen-Hoffman Theory for Polymer Crystallization

Overview

This package computes secondary nucleation constants from DSC (Differential Scanning Calorimetry) measurements (Enthalpy vs. Time) using the Lauritzen-Hoffman theory.

📄 Theory and Background

Features

• Analyze DSC data to calculate secondary nucleation constants.
• Fit experimental data using the Lauritzen-Hoffman growth model.
• Output key parameters such as the secondary nucleation constant (kg) and the logarithm of the pre-exponential factor (lgI0).

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Installation

Install the package using pip:

pip install lauritzen-hoffman

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Example Usage

Import the Module

from lauritzen_hoffman.linear_rate import lh_growth_model

Input Parameters

1. file_path: Path to your DSC (Differential Scanning Calorimetry) measurement file.
2. initial_guess: Initial guess values for optimization.
3. Constants and Data:
   • Area: Crystalline surface area used in calculations.
   • T_range: List of temperatures at which growth is analyzed.
   • U: Activation energy for transport.
   • Tinf: Temperature below which molecular motion stops.
   • T0m: Equilibrium melting temperature.
   • R: Universal gas constant.

Example Code

from lauritzen_hoffman.linear_rate import lh_growth_model

# Define file path 
file_path = 'path_to_your_dsc_data.csv'

# Set initial guess 
initial_guess = [value1, value2, ...]

# Conditions
Area = 1.300149 * (10 ** -12)  # Example area in square meters
T_range = [T1, T2, T3, ...]   # List of temperature values in Kelvin
U = your_value                 # Activation energy for transport (e.g., kJ/mol)
Tinf = your_value              # Theoretical temperature below which no motion occurs (Kelvin)
T0m = your_value               # Equilibrium melting temperature (Kelvin)
R = 1.99                       # Universal gas constant (J/(mol*K))

# Run
kg, lgI0 = lh_growth_model(file_path, initial_guess, T_range, Area, U, R, Tinf, T0m)

# Results
print("Secondary nucleation constant, kg:", kg)
print("Logarithm of pre-exponential factor, lgI0:", lgI0)

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Parameters

• file_path: Path to the DSC measurement file.
• initial_guess: A list of initial guesses for the parameters being optimized.
• Area: Crystalline surface area (default example: 1.300149 * (10 ** -12) m²).
• T_range: List of temperature values (Kelvin).
• U: Activation energy for molecular transport.
• Tinf: Temperature below which molecular motion stops.
• T0m: Equilibrium melting temperature (Kelvin).
• R: Universal gas constant (J/(mol*K)).

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Outputs

The function computes:

1. kg: The secondary nucleation constant.
2. lgI0: Logarithm of the pre-exponential factor.