Four-dimensional polymer collapse: pseudo-first-order transition in interacting self-avoiding walks

Area of Science:

• Polymer physics
• Statistical mechanics
• Computational chemistry

Background:

• The coil-globule transition is a fundamental phenomenon in polymer science.
• Previous work established evidence for this transition in a four-dimensional model.
• Understanding polymer collapse is crucial for predicting material properties.

Purpose of the Study:

• To investigate the canonical lattice model of polymer collapse using Monte Carlo simulations.
• To characterize the nature of the collapse transition in four dimensions.
• To reconcile finite-size transition characteristics with thermodynamic limit behavior.

Main Methods:

• Monte Carlo simulations of interacting self-avoiding walks on a lattice.
• Analysis of finite-size scaling behavior of the polymer collapse transition.
• Application of Lifshitz-Grosberg-Khokhlov theory in four dimensions.

Main Results:

• The polymer collapse exhibits a rounded first-order phase transition for finite polymer lengths.
• A "straight theta point" (critical Gaussian state) is identified, approached by transition temperatures.
• Finite-size effects cause the transition to appear rounded, masking the second-order nature in the thermodynamic limit.

Conclusions:

• The apparent first-order transition is an artifact of finite chain length and finite temperature.
• In the thermodynamic limit, the polymer collapse transitions to a mean-field second-order transition.
• The Lifshitz theory provides a framework for understanding polymer collapse above the upper critical dimension (d=3).