Role of length polydispersity in the phase behavior of freely rotating hard-rectangle fluids

Ariel Díaz-De Armas and Yuri Martínez-Ratón
Phys. Rev. E 95, 052702 – Published 22 May 2017

Abstract

We use the density-functional formalism, in particular the scaled-particle theory, applied to a length-polydisperse hard-rectangle fluid to study its phase behavior as a function of the mean particle aspect ratio κ0 and polydispersity Δ0. The numerical solutions of the coexistence equations are calculated by transforming the original problem with infinite degrees of freedoms to a finite set of equations for the amplitudes of the Fourier expansion of the moments of the density profiles. We divide the study into two parts. The first one is devoted to the calculation of the phase diagrams in the packing fraction η0κ0 plane for a fixed Δ0 and selecting parent distribution functions with exponential (the Schulz distribution) or Gaussian decays. In the second part we study the phase behavior in the η0Δ0 plane for fixed κ0 while Δ0 is changed. We characterize in detail the orientational ordering of particles and the fractionation of different species between the coexisting phases. Also we study the character (second vs first order) of the isotropic-nematic phase transition as a function of polydispersity. We particularly focus on the stability of the tetratic phase as a function of κ0 and Δ0. The isotropic-nematic transition becomes strongly of first order when polydispersity is increased: The coexistence gap widens and the location of the tricritical point moves to higher values of κ0 while the tetratic phase is slightly destabilized with respect to the nematic one. The results obtained here can be tested in experiments on shaken monolayers of granular rods.

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  • Received 7 February 2017

DOI:https://doi.org/10.1103/PhysRevE.95.052702

©2017 American Physical Society

Physics Subject Headings (PhySH)

Polymers & Soft MatterStatistical Physics & Thermodynamics

Authors & Affiliations

Ariel Díaz-De Armas* and Yuri Martínez-Ratón

  • Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain

  • *ardiaza@math.uc3m.es
  • yuri@math.uc3m.es

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Issue

Vol. 95, Iss. 5 — May 2017

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