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Unlike ionic or small covalent molecules, polymers do not form crystalline solids due to the diffusion limitations of their long-chain structures. However, polymers contain microscopic crystalline domains separated by amorphous domains.
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Partition function zeros and phase transitions for a square-well polymer chain.

Mark P Taylor1, Pyie Phyo Aung, Wolfgang Paul

  • 1Department of Physics, Hiram College, Hiram, Ohio 44234, USA. taylormp@hiram.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 16, 2013
PubMed
Summary
This summary is machine-generated.

Analyzing partition function zeros reveals distinct patterns for polymer chain transitions. These signatures help identify coil-globule, globule-crystal, and coil-crystal phase changes in flexible polymer models.

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Area of Science:

  • Statistical Mechanics
  • Polymer Physics
  • Computational Chemistry

Background:

  • Flexible polymer chains exhibit complex phase transitions, including coil-globule, globule-crystal, and direct coil-crystal.
  • Understanding these transitions is crucial for predicting polymer behavior in various conditions.

Purpose of the Study:

  • To identify and characterize the signatures of different phase transitions in flexible polymer chains using partition function zeros.
  • To determine transition temperatures and critical exponents for these transitions.

Main Methods:

  • Computation of partition function zeros for flexible square-well polymer chains up to length 256.
  • Analysis of the complex-plane distribution of these zeros to identify transition signatures.
  • Application of finite-size scaling analysis to determine thermodynamic limit transition temperatures.

Main Results:

  • Freezing transitions (globule-crystal, coil-crystal) are marked by circular rings of uniformly spaced zeros.
  • The coil-globule collapse transition is indicated by an elliptical horseshoe segment of zeros.
  • Increasing chain length enhances root density and shifts leading roots towards the real axis, allowing for finite-chain transition temperature determination.

Conclusions:

  • Partition function zeros provide clear, distinct signatures for different polymer phase transitions.
  • The identified signatures and calculated exponents (φ≈0.76(2), α≈0.66(2)) are consistent with a second-order phase transition for the collapse.
  • This method offers a robust approach for characterizing polymer phase behavior and determining critical parameters.