The orientational phase transitions that occur in the deposition of longitudinal polymers of length $k$ (in terms of lattice units) are characterized by information theory techniques. We calculate the absolute value of an order parameter $\delta$, which weights the relative orientations of the deposited rods, which varies between 0.0 (random orientation) and 1.0 (fully oriented in either of the two equivalent directions in an $L\times L$ square lattice). A Monte Carlo (MC) algorithm is implemented to induce a dynamics allowing for accommodation of the rods for any given density or coverage $\theta$ (ratio of the occupied sites over all the sites in the lattice). The files storing $\delta \left(t\right)$ (with time $t$ measured in MC steps) are then treated by data recognizer wlzip based on data compressor techniques yielding the information content measured by a parameter $\eta \left(\theta \right)$. This allows us to recognize two maxima separated by a well-defined minimum for $\eta \left(\theta \right)$ provided $k\ge 7$. The first maximum is associated with an isotropic-nematic ($I\text{−}N$) phase transition occurring at intermediate density, while the second maximum is associated with some kind of nematic-isotropic transition at high coverage. In the cases of $k<7$, the curves for $\eta \left(\theta \right)$ are almost constant, presenting a very broad maximum which can hardly be associated with a phase transition. The study varies $L$ and $k$, allowing for a basic scaling of the found critical densities towards the thermodynamic limit. These calculations confirm the tendency obtained by different methods in the case of the intermediate-density $I\text{−}N$ phase transition, while this tendency is established here in the case of the high-density phase transition.

• Received 24 May 2017

DOI:https://doi.org/10.1103/PhysRevE.96.062133