Partition function zeros and finite size scaling for polymer adsorption

Area of Science:

• Statistical Mechanics
• Polymer Physics
• Surface Science

Background:

• Understanding polymer behavior at surfaces is crucial in fields ranging from materials science to biophysics.
• The Yang-Lee theory provides a framework for analyzing phase transitions through the zeros of the partition function.

Purpose of the Study:

• To compute the partition function zeros for flexible polymer chains tethered to an attractive flat surface.
• To investigate the structure of these zeros and their relation to the polymer adsorption transition.
• To determine critical exponents and scaling functions governing the adsorption phenomenon.

Main Methods:

• Employed a bond-fluctuation model for simulating polymer chains up to N = 1536.
• Utilized Wang-Landau sampling to obtain the density of states for tethered chains.
• Applied finite-size scaling theory to analyze partition function zeros.

Main Results:

• Partition function zeros form a symmetric, circular boundary with flaring tails, defining a root-free zone consistent with Yang-Lee theory.
• The analysis precisely located the polymer adsorption transition at a reduced temperature Tc(*)=1.027(3) with crossover exponent ϕ = 0.515(25).
• Determined critical exponents for the order parameter (β̃=0.97(5)) and specific heat (α = 0.03(4)).

Conclusions:

• The structure of partition function zeros accurately predicts the polymer adsorption transition point and critical behavior.
• Finite-size scaling analysis of zeros provides a robust method for determining thermodynamic properties.
• A universal scaling function for surface contacts was successfully constructed.