Linear Polymer Chain Diffusion in Semi-flexible Polymer Network: A Dissipative Particle Dynamics Study

Linear polymer chains transport in the crowded biological environment is profoundly important to biomedical engineering and nanotechnology. Cytoskeleton, which can be modelled as a semi-flexible polymer network, acts as a barrier when the linear polymers diffuse inside the cell. The diffusion of linear polymers with length N in this polymer network is investigated by the dissipative particle dynamics (DPD) in the present study. Rouse theory is applied to analyze the conformational dynamics of the linear polymers based on the numerical results. It is found that the geometric constraint length Na is a crucial parameter to describe the role of the network of the polymer diffusion. Analyses on the Rouse modes show that, in short wavelength regime, the relaxation time obtained in numerical simulation follows the the prediction of the Rouse theory. As the increasing of the wavelength, the linear polymer exhibits a transition from reptation behavior to the spatially homogeneous behavior at critical length scale Na, which is illustrated by different scaling laws dependent on wavelength. Based the analyses on the Rouse modes and mean square displacements of the linear polymer, we present a non-dimensional conformational dynamics function dependent on time, with which a scaling law is proposed to predict the long time diffusivity of the linear polymer in semi-flexible polymer network with different mesh size. It is shown that the prediction is well consistent with our DPD simulation results.