Self-Avoiding Random Walks as a Model to Study Athermal Linear Polymers under Extreme Plate Confinement.

Area of Science:

• Computational physics and polymer science.
• Statistical mechanics of confined systems.

Background:

• Understanding polymer behavior under extreme confinement is crucial for materials science.
• Bulk polymer crystallization densities are well-established, but confined systems present unique challenges.
• Phase transitions in polymers are driven by configurational entropy.

Purpose of the Study:

• To investigate crystal nucleation and growth in freely-jointed polymer chains confined between parallel plates.
• To map confined polymer chains to self-avoiding walks (SAWs) on cubic lattices.
• To determine the configurational entropy driving phase transitions and thermodynamic stability of crystal morphologies.

Main Methods:

• Monte Carlo (MC) simulations utilizing chain-connectivity-altering moves and a wall-displacement algorithm.
• Analysis of local structure using the characteristic crystallographic element (CCE) norm.
• Mapping confined polymer chains to self-avoiding random walks (SAWs) on simple, body-centered, and face-centered cubic lattices.

Main Results:

• Crystal nucleation and growth detected at packing densities significantly lower than in bulk analogs.
• Enumeration of all possible SAWs (conformations) for various chain lengths, lattice types, and confinement levels.
• Size distributions calculated for SAWs, enabling prediction of long, entangled chain behavior via growth formulas.

Conclusions:

• Extreme confinement drastically alters polymer crystallization behavior, initiating it at lower densities.
• The self-avoiding walk (SAW) model provides a framework to analyze polymer conformations and predict phase transitions.
• Configurational entropy is identified as the key factor governing the observed phase transitions and thermodynamic stability of confined polymer crystals.