Transitions to Ordered Phases in Systems Containing Rod-like Particles: III. Four Fundamental Reasons for the Predictive Deficiencies of Discrete Lattice Models

Abstract

This paper identifies and discusses four fundamental causes for the discrepancy between the entropy predictions of our new continuous-placement Monte Carlo (CMC) approach and the discrete lattice model (DLM) of Flory and Ronca. The DLM allows rods to cross, enables rods to fit too easily into tight spaces, does not account for unoccupiable (wasted) space, and neglects the ingrowth of short-range order. Increasing resolution can eliminate the first two shortcomings from the DLM. To account for wasted space in the DLM, it will be necessary to derive a more complex expression for combinatorie entropy. To properly accommodate the effect of short-range order, the calculation of both combinatorie and orientational entropy must be improved.

Key Words:

• lattice model
• Monte Carlo
• rod-like particles
• short-range order
• two-dimensional
• vacancies