Swelling of particle-encapsulating random manifolds

Area of Science:

• Statistical mechanics
• Soft matter physics
• Thermodynamics

Background:

• Studying the statistical mechanics of closed random manifolds with fluctuating volumes.
• Investigating the influence of encapsulated non-interacting particles on manifold properties.
• Understanding the relationship between manifold swelling and particle number.

Purpose of the Study:

• To develop a unified description of swollen manifolds encapsulating particles.
• To determine the thermodynamic equivalence between particle-induced and pressure-induced swelling.
• To identify conditions under which these two swelling mechanisms differ.

Main Methods:

• Applying scaling analysis to theoretical models of random manifolds.
• Conducting Monte Carlo simulations for two specific model systems: a 2D self-avoiding ring and a 3D self-avoiding fluid vesicle.
• Comparing simulation results with theoretical predictions.

Main Results:

• A universal scaling law was identified for mean volume increase with particle number.
• Particle-induced swelling was found to be thermodynamically inequivalent to pressure-induced swelling in the 3D vesicle model.
• Thermodynamic equivalence was observed in the 2D ring model.

Conclusions:

• The swelling of random manifolds due to encapsulated particles exhibits distinct thermodynamic behavior compared to pressure-induced swelling.
• The dimensionality and nature of the manifold system are critical in determining the thermodynamic equivalence of swelling mechanisms.
• The findings provide a framework for distinguishing between different swelling phenomena in physical systems.