Phase transition in diffusion limited aggregation with patchy particles in two dimensions

• A 2D DLA model with patchy interactions is proposed.
• The growth rate of clusters depends on the patch size of the particles.
• A non-equilibrium phase transition is observed.
• The phase transition in patchy-DLA belongs to directed percolation universality class.

The influence of patchy interactions on diffusion-limited aggregation (DLA) has been investigated by computer simulations. In this model, the adsorption of the particle is irreversible, but the adsorption occurs only when the ‘sticky patch’ makes contact with the sticky patch of a previously adsorbed particle. As we vary the patch size, growth rate of the cluster decreases, and below a well-defined critical patch size, pcpc the steady state growth rate goes to zero. The system reaches an absorbing phase producing a non-equilibrium continuous phase transition. The order parameter close to the critical value of the patch size shows a power law behavior ρ(∞)∼(p−pc)βρ(∞)∼(p−pc)β, where β=0.2840β=0.2840. We have found that the value of the critical exponent convincingly shows that this transition in patchy DLA belongs to the directed percolation universality class.