Phase transitions in the confined growth of chains formed by self-avoiding hard spheres

We show that phase transitions occur in the confined growth of chains formed by self-avoiding hard spheres. Planar growth arises from the stochastic interplay of two simple opposing mechanisms: enforced connectivity and self-avoidance between spheres. Depending on the value of parameter T that sets the tendency of growth along a definite direction, the structures either settle into a box-limited or a self-trapped configuration. We established that a T value exists where fully grown structures are likely to be bigger for the same confinement area. The said T value is independent of confinement area for sufficiently large boxes and it is near a critical point for a phase transition between the box-limited configuration and the self-trapped configuration.