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Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial,...
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Phase behavior of hard cylinders.

Joyce T Lopes1, Flavio Romano2, Eric Grelet3

  • 1Universidade Estadual de Campinas, Faculdade de Engenharia Química, Departamento de Engenharia de Sistemas Químicos, Campinas, Brazil.

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|March 16, 2021
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Summary

This study maps the phase diagram for hard cylindrical particles. For prolate cylinders (L/D > 1), nematic and smectic phases emerge. For oblate cylinders (L/D < 1), cubatic, nematic, and columnar phases are stable.

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Area of Science:

  • Physics
  • Materials Science
  • Computational Chemistry

Background:

  • Understanding the phase behavior of anisotropic particles is crucial for materials science.
  • Cylindrical particles exhibit complex phase diagrams influenced by their aspect ratio.
  • Previous studies on hard cylinders have provided partial phase diagrams, necessitating a comprehensive investigation.

Purpose of the Study:

  • To computationally map the complete phase diagram of hard cylindrical particles.
  • To investigate the influence of particle aspect ratio (L/D) on phase behavior.
  • To identify stable and metastable phases and their transition points.

Main Methods:

  • Isobaric Monte Carlo simulations were employed.
  • An improved algorithm for detecting cylinder overlap was utilized.
  • Simulations covered both prolate (L/D > 1) and oblate (L/D < 1) geometries.

Main Results:

  • For prolate cylinders, isotropic (I), nematic (N), smectic (SmA), and crystal (X) phases were identified, with I-N-SmA and I-SmA-X triple points.
  • A metastable columnar (C) phase was observed for prolate cylinders.
  • For oblate cylinders, stable intermediate phases included cubatic (Cub), nematic (N), and columnar (C), with triple points I-N-Cub, N-Cub-C, and I-Cub-C.

Conclusions:

  • The study provides a comprehensive phase diagram for hard cylindrical particles, revealing distinct behaviors for prolate and oblate shapes.
  • The findings highlight the stability of cubatic, nematic, and columnar phases in oblate systems.
  • This work offers a foundation for more complex models with potential applications in biological systems like viruses and nucleosomes.