PPT Slide
Computations are performed with 1936 particles. Mixture is symmetric, i.e. sa =sb =s and molar fractions of 'A' and 'B' particles are equal (xa=xb=1/2). For this case osmotic pressure effect does not play a role, and the system is driven only by non-additivity. For each value of non-additivity parameter (a) and density (r) 10000 cycles over all particles are performed. From each simulation 200 snapshots are recorded for analysis.
Simulations have been performed for nine different values of a in the range (0.01;1.0). Each simulation starts from the most dense state and the density is decreased after 10000 cycles, until a complete mixing is observed. At the initial state 'A' and 'B' particles are completely separated.
We have observed demixing transition for all values of a. In order to characterize the phase transition we have introduced an order parameter ?, which we refer as the mixing parameter. It is calculated as follows. Choose a particle, count the number of particles of the same type within a cut off distance (Rc). Divide it by the total number of particles within Rc . Finally, take the average over all the particles.
Rc is chosen as 1/10 of the box length, in order to keep the average number of particles within the cut off distance approximately constant for different density values. In the completely demixed case ?=1.0 and in the completely mixed case ?=0.5. However due to finite size effects ? does not reach these extreme limits.
The phase transition is clearly seen in figure 4. The value of mixing parameter (?) is plotted vs. density for different values of non-additivity parameter. As non-additivity parameter decreases the critical density increases.