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Register a new userStatistical thermodynamics of long straight rigid rods on triangular lattices: nematic order and adsorption thermodynamic functions
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The statistical thermodynamics of straight rigid rods of length $k$ on triangular lattices was developed on a generalization in the spirit of the lattice-gas model and the classical Guggenheim-DiMarzio approximation. In this scheme, the Helmholtz free energy and its derivatives were written in terms of the order parameter $delta$, which characterizes the nematic phase occurring in the system at intermediate densities. Then, using the principle of minimum free energy with $delta$ as a parameter, the main adsorption properties were calculated. Comparisons with Monte Carlo simulations and experimental data were performed in order to evaluate the reaches and limitations of the theoretical model.
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Using Monte Carlo simulations and finite-size scaling analysis, the critical behavior of self-assembled rigid rods on triangular and honeycomb lattices at intermediate density has been studied. The system is composed of monomers with two attractive (sticky) poles that, by decreasing temperature or increasing density, polymerize reversibly into chains with three allowed directions and, at the same time, undergo a continuous isotropic-nematic (IN) transition. The determination of the critical exponents, along with the behavior of Binder cumulants, indicate that the IN transition belongs to the q=1 Potts universality class.
Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with mean field (MF) and real space renormalization group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results.
Numerical simulations and finite-size scaling analysis have been carried out to study the percolation behavior of straight rigid rods of length $k$ ($k$-mers) on two-dimensional square lattices. The $k$-mers, containing $k$ identical units (each one occupying a lattice site), were adsorbed at equilibrium on the lattice. The process was monitored by following the probability $R_{L,k}(theta)$ that a lattice composed of $L times L$ sites percolates at a concentration $theta$ of sites occupied by particles of size $k$. A nonmonotonic size dependence was observed for the percolation threshold, which decreases for small particles sizes, goes through a minimum, and finally asymptotically converges towards a definite value for large segments. This striking behavior has been interpreted as a consequence of the isotropic-nematic phase transition occurring in the system for large values of $k$. Finally, the universality class of the model was found to be the same as for the random percolation model.
Using Monte Carlo simulations and finite-size scaling analysis, the critical behavior of attractive rigid rods of length k (k-mers) on square lattices at intermediate density has been studied. A nematic phase, characterized by a big domain of parallel k-mers, was found. This ordered phase is separated from the isotropic state by a continuous transition occurring at a intermediate density theta_c, which increases linearly with the magnitude of the lateral interactions.
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Anandamohan Ghosh
, Deepak Dhar (Department of Theoretical Physics
, n Tata Institute of Fundamental Research
2006
We argue that a system of straight rigid rods of length k on square lattice with only hard-core interactions shows two phase transitions as a function of density, rho, for k >= 7. The system undergoes a phase transition from the low-density disordered phase to a nematic phase as rho is increased from 0, at rho = rho_c1, and then again undergoes a reentrant phase transition from the nematic phase to a disordered phase at rho = rho_c2 < 1.
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