Temperature-dependent structural behavior of self-avoiding walks on three-dimensional Sierpinski sponges

Area of Science:

• Statistical Mechanics
• Polymer Physics
• Materials Science

Background:

• Polymers adsorbed on disordered media exhibit complex statistical behavior.
• Self-avoiding walks (SAWs) are crucial models for polymer chains.
• Fractal structures offer unique environments for studying physical phenomena.

Purpose of the Study:

• Investigate the statistical properties of SAWs on Sierpinski cubic lattices at finite temperatures.
• Model polymers absorbed on a disordered medium using a deterministic fractal energy landscape.
• Analyze the scaling behavior of the end-to-end distance for SAWs.

Main Methods:

• Simulated SAWs with up to N=1280 steps on 3D Sierpinski sponge lattices.
• Introduced a fractal energy landscape with two types of sites (energy 0 and ε>0).
• Calculated the probability distribution function and studied scaling behavior of the end-to-end distance.

Main Results:

• Recovered known SAW behavior on cubic lattices at high temperatures (T → ∞).
• Obtained scaling exponents at low temperatures (T → 0) and compared them with exact enumeration results.
• Found that 3D SAW behavior at finite temperatures is intermediate between 2D and 3D limits, with exponents depending on temperature.

Conclusions:

• The temperature significantly impacts the structural behavior and scaling exponents of SAWs on fractal lattices.
• Sierpinski cubic lattices provide a valuable model for understanding polymer adsorption on disordered surfaces.
• The study highlights the nontrivial dependence of characteristic exponents on temperature in fractal environments.