Abstract
We study the phase behavior of the Zwanzig model of suspensions of hard rods, allowing for polydispersity in the lengths of the rods. In spite of the simplified nature of the model (rods are restricted to lie along one of three orthogonal axes), the results agree qualitatively with experimental observations: the coexistence region broadens significantly as the polydispersity increases, and strong fractionation occurs, with long rods found preferentially in the nematic phase. These conclusions are obtained from an analysis of the exact phase equilibrium equations. In the second part of the paper, we consider the application of the recently developed “moment free energy method” to the polydisperse Zwanzig model. Even though the model contains nonconserved densities due to the orientational degrees of freedom, most of the exactness statements (regarding the onset of phase coexistence, spinodals, and critical points) derived previously for systems with conserved densities remain valid. The accuracy of the results from the moment free energy increases as more and more additional moments are retained in the description. We show how this increase in accuracy can be monitored without relying on knowledge of the exact results, and discuss an adaptive technique for choosing the extra moments optimally.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
