Non-Equilibrium Wigner Function and Application to Model of Catalyzed Polymerization.

Area of Science:

• Quantum mechanics and statistical mechanics
• Chemical kinetics and molecular dynamics

Background:

• Investigates non-equilibrium quantum dynamics for a particle in a potential and heat bath.
• Extends previous analysis to model molecular chain polymerization in 3D.

Purpose of the Study:

• Develop a novel quantum-classical model for molecular chain growth (polymerization).
• Analyze the mean first passage time (MFPT) for atom binding to a molecular chain, catalyzed process.
• Connect microscopic dynamics to macroscopic chemical reaction rates.

Main Methods:

• Utilizes a mixed non-equilibrium quantum-classical Wigner-Liouville function and dynamical equations.
• Applies approximations including continued fractions, infinite series, and Smoluchowski equation.
• Employs classical statistical mechanics for molecular chains and catalysts, quantum mechanics for atoms and bindings.

Main Results:

• Derives a general hierarchy for non-equilibrium moments and obtains a new solution.
• Obtains an approximate Smoluchowski equation for the atom's binding dynamics.
• Calculates MFPT for catalyzed atom binding, showing consistency with the Arrhenius formula.

Conclusions:

• The developed model provides a quantum-classical framework for polymerization processes.
• The MFPT results validate the model's ability to predict chemical reaction rates.
• This approach bridges quantum phenomena with macroscopic chemical kinetics.