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Investigating Single Molecule Adhesion by Atomic Force Spectroscopy
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Partition function zeros and finite size scaling for polymer adsorption.

Mark P Taylor1, Jutta Luettmer-Strathmann2

  • 1Department of Physics, Hiram College, Hiram, Ohio 44234, USA.

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|November 29, 2014
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Summary

We computed partition function zeros for polymer chains on a surface, revealing a circular boundary defining a root-free zone. This analysis precisely locates the polymer adsorption transition point and critical exponents.

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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.