Thermodynamics of a binary monolayer of Ising dipolar particles

Thermodynamic behavior of a binary monolayer of Ising dipolar particles is studied using numerical simulation. The thermal equilibrium states of the system under the canonical ensemble are observed. The boundary of gas-liquid phase is determined from the power law growth of critical clusters. But that temperature is slightly lower than that of solidification. So it means that this system does not have a liquid phase. This system is also studied theoretically using virial expansion. The coefficients obtained from standard virial expansion, however, do not show any phase transition. An improvement of the virial expansion is also given by taking tetragonal local structures of alternate types of particles into consideration. Such structures are observed within critical clusters of our simulation. The thermodynamic state equation obtained from the improved virial expansion agrees well with the simulation result, and this expansion also shows that the critical point is almost at the same temperature with solidification. These results suggest that not simply the strength of attractive force by the dipole interaction but a typical configuration caused by the binary condition of this system plays a dominant role in phase transitions.

Figure 1

(Color online) Snapshots from the equilibrium state at $\varphi =0.125$, $T=0.100$ (left) and at $\varphi =0.125$, $T=0.060$ (right) are shown. Many clusters with finite size move around, instead of aggregating into a large cluster. Each inset shows a snapshot focused on some typical clusters.

Figure 2

(Color online) Scaling plot of the average cluster size with Eq. (6) is shown.

Figure 3

(Color online) Scaling plot of the correlation length with Eq. (10) is shown.

Figure 4

(Color online) Formation of a solid cluster with square lattice order of alternating particles at $N=1600$, $\varphi =0.125$, and $T=0.055$. The inset shows an inner part of the largest cluster.

Figure 5

(Color online) Average cluster size (above) and the orientational order ${\varphi }_4$ (below) around the solidification are shown. Each plot is the time average after the system reached equilibrium state.

Figure 6

Outline of the $\varphi -T$ phase diagram.

Figure 7

(Color online) State equation curves calculated by virial expansion up to third order are displayed.

Figure 8

(Color online) Snapshot focused on the inner part of a cluster of critical region is shown. ($\varphi =0.125$, $T=0.0574$, and $N=6400$.)

Figure 9

(Color online) Left, schematic drawing of the tetramer model and aggregation under this model (mixture of tetramers and monomers). Right, cell divided model for solidification.

Figure 10

(Color online) Optimized value of $\alpha$ and the pressure curves against $\varphi$ are shown. Our tetramer model analysis (second order) agrees much better with the simulation compared to the standard virial expansion.

Figure 11

(Color online) Gibbs free energy calculated by two kinds of models: the tetramer model (low density region) and the cell divided model (high density).