Dynamics of self-propelled tracer particles inside a polymer network

The transport of tracer particles through mesh-like environments such as biological hydrogels and polymer matrices is ubiquitous in nature. These tracers can be passive, such as colloids, or active (self-propelled), for example, synthetic nanomotors or bacteria. Computer simulations in principle could be extremely useful in exploring the mechanism of the active transport of tracer particles through mesh-like environments. Therefore, we construct a polymer network on a diamond lattice and use computer simulations to investigate the dynamics of spherical self-propelled particles inside the network. Our main objective is to elucidate the effect of the self-propulsion on the tracer particle dynamics as a function of the tracer size and the stiffness of the polymer network. We compute the time-averaged mean-squared displacement (MSD) and the van-Hove correlations of the tracer. On the one hand, in the case of a bigger sticky particle, the caging caused by the network particles wins over the escape assisted by the self-propulsion. This results an intermediate-time subdiffusion. On the other hand, smaller tracers or tracers with high self-propulsion velocities can easily escape from the cages and show intermediate-time superdiffusion. The stiffer the network, the slower the dynamics of the tracer, and bigger tracers exhibit longer lived intermediate time superdiffusion, since the persistence time scales as similar to sigma(3), where sigma is the diameter of the tracer. At the intermediate time, non-Gaussianity is more pronounced for active tracers. At the long time, the dynamics of the tracer, if passive or weakly active, becomes Gaussian and diffusive, but remains flat for tracers with high self-propulsion, accounting for their seemingly unrestricted motion inside the network.