Self-assembly of patchy particles into polymer chains: a parameter-free comparison between Wertheim theory and Monte...

Area of Science:

• Statistical mechanics
• Soft matter physics
• Computational chemistry

Background:

• Equilibrium polymerization is crucial for understanding self-assembly in various systems.
• Existing theories often require fitting parameters, limiting predictive power.
• Simple models are needed to rigorously test theoretical frameworks.

Purpose of the Study:

• To numerically investigate a simplified model of equilibrium polymerization.
• To compare simulation results with predictions from Wertheim perturbation theory.
• To establish a parameter-free framework for predicting self-assembly properties.

Main Methods:

• Numerical simulations of a fluid with hard-core repulsion and sticky poles.
• Application of Wertheim perturbation theory for theoretical predictions.
• Calculation of thermodynamic properties including energy, order parameter, and chain statistics.

Main Results:

• Simulation data showed remarkable agreement with Wertheim theory predictions.
• The theory accurately predicted thermodynamic properties across the polymerization transition.
• Key properties like average chain length and static structure factor were well-reproduced.

Conclusions:

• Wertheim perturbation theory provides a robust, parameter-free predictive tool for self-assembling systems.
• The simple sticky-particle model serves as an excellent test case for theoretical approaches.
• This work advances the analytic understanding of equilibrium polymerization and self-assembly.