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Polymers in long-range-correlated disorder.

V Blavats'ka1, C von Ferber, Y Holovatch

  • 1Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
PubMed
Summary

We investigated polymer scaling properties in disordered media. Our findings show that long-range correlated defects significantly impact polymer behavior, introducing unique scaling exponents.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Polymer Physics

Background:

  • Polymers exhibit complex scaling properties influenced by their environment.
  • Quenched disorder, particularly with power-law correlations, is crucial in understanding phase transitions.
  • The relevance of such disorder for polymer systems was previously less understood.

Purpose of the Study:

  • To investigate the scaling properties of polymers in a d-dimensional medium with long-range correlated quenched defects.
  • To determine if power-law correlated disorder, relevant in magnetic systems, also affects polymer behavior.
  • To calculate critical exponents and correction-to-scaling exponents for polymers under this type of disorder.

Main Methods:

  • Field-theoretical renormalization group approach.

Related Experiment Videos

  • Calculations performed using a double expansion in epsilon=4-d and delta=4-a up to one-loop order.
  • Two-loop approximation calculations in a fixed dimension (d=3) for 2<=a<=3.

    • Main Results:

    • Strong evidence suggests that long-range correlated disorder is relevant for polymer systems.
    • The asymptotic behavior of self-avoiding walks in 3D with correlated disorder is governed by distinct exponents.
    • Estimates for the nu and gamma exponents, and the correction-to-scaling exponent omega were obtained.

    Conclusions:

    • Long-range correlated disorder significantly alters polymer scaling behavior.
    • The study provides crucial exponents characterizing polymers in such complex environments.
    • The findings extend to the general m-vector model, offering broader applicability.