Predicting Ion Sequestration in Charged Polymers with the Steepest-Entropy-Ascent Quantum Thermodynamic Framework

Area of Science:

• Quantum thermodynamics
• Environmental chemistry
• Materials science

Background:

• Rare-earth element (REE) sequestration is critical for environmental remediation and resource recovery.
• Polymer-based adsorbents offer potential for efficient REE capture from aqueous solutions.
• Understanding the dynamic binding mechanisms of REEs to polymers is essential for optimizing sequestration strategies.

Purpose of the Study:

• To investigate the effectiveness of multi-chain polyethyleneimine-methylenephosphonic acid in sequestering rare-earth ions (Eu³⁺).
• To model the binding kinetics and thermodynamic pathways of europium ion sequestration using a quantum thermodynamic framework.
• To correlate polymer structural evolution with sequestration efficiency.

Main Methods:

• Application of the steepest-entropy-ascent quantum thermodynamic framework.
• Modeling binding kinetics using a thermodynamic equation of motion on a discrete energy eigenstructure.
• Generation of energy eigenstructure via non-Markovian Monte Carlo simulation.
• Analysis of polymer physical descriptors (radius of gyration, tortuosity) using a second Monte Carlo simulation.

Main Results:

• The study establishes a unique thermodynamic path for polymer-mediated europium sequestration.
• Sequestration fraction is inversely proportional to the total system energy; lower energy leads to higher sequestration.
• Polymer structural evolution, including radius of gyration and tortuosity, was visualized during the sequestration process.
• Kinetics are governed by the steepest-entropy-ascent principle, dictating the path from non-equilibrium states.

Conclusions:

• Multi-chain polyethyleneimine-methylenephosphonic acid demonstrates significant potential for rare-earth ion sequestration.
• The quantum thermodynamic framework provides a robust method for understanding and optimizing ion-binding kinetics.
• System energy and polymer dynamics are key factors influencing the efficiency of rare-earth ion capture.