Role of length-polydispersity on the phase behavior of freely-rotating hard-rectangle fluid
英文摘要：
We used the Density Functional formalism, in particular the Scaled Particle Theory, applied to a length-polydisperse hard-rectangular fluid to study its phase behavior as a function of the mean particle aspect ratio ($κ_0$) and polydispersity ($Δ_0$). The numerical solutions of the coexistence equations were 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 divided the study into two parts: The first one is devoted to the calculation of the phase diagrams in the packing fraction ($η_0$)- $κ_0$ plane for a fixed $Δ_0$ and selecting parent distribution functions with exponential (the Schulz distribution) or Gaussian decays. In the second part we study the phase behavior in the $η_0$-$Δ_0$ plane for fixed $κ_0$ while $Δ_0$ 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 focused on the stability of the Tetratic phase as a function of $κ_0$ and $Δ_0$. The Isotropic-Nematic transition becomes strongly of first order when polydispersity is increased: the coexisting gap widens and the location of the tricritical point moves to higher values of $κ_0$ 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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