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Partition-function-zero analysis of polymer adsorption for a continuum chain model.

Mark P Taylor1, Samip Basnet1, Jutta Luettmer-Strathmann2

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

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|October 16, 2021
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Summary
This summary is machine-generated.

This study investigates polymer adsorption using partition function zeros, revealing universal critical behavior. Key scaling exponents and approach angles were found to be independent of interaction range, confirming universality across models.

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Area of Science:

  • Polymer Physics
  • Statistical Mechanics
  • Phase Transitions

Background:

  • Polymer adsorption exhibits universal critical behavior, often studied using partition function zeros.
  • Continuum models offer a way to explore a continuous range of interactions and compare with lattice models.

Purpose of the Study:

  • To investigate the adsorption transition of a continuum polymer chain.
  • To analyze the behavior of partition function zeros for a tethered hard-sphere chain.
  • To compare results with existing lattice model studies and confirm universality.

Main Methods:

  • Computed partition function (Fisher) zeros for a tangent-hard-sphere N-mer chain up to N=1280.
  • Utilized an attractive square-well potential with varying interaction ranges (0.01≤λ≤2.0).
  • Applied finite-size scaling analysis to determine critical points, scaling exponents (ϕ), and approach angles (θc).

Main Results:

  • Leading partition function zeros approach the critical point following a scaling law w₁(N)-yc∼N⁻<0xC2><0xB3>.
  • The critical point (yc) and critical temperature (Tc) decrease with increasing interaction range (λ).
  • The scaling exponent ϕ=0.479(9) and approach angle θc=56.8(1.4)° were found to be independent of λ.

Conclusions:

  • The study demonstrates the universality of critical behavior in polymer adsorption across lattice and continuum models.
  • The computed values for ϕ and θc align with high-precision lattice model results.
  • Partition function zeros provide a robust method for analyzing polymer adsorption transitions.