Double-Spring Model for Nanoparticle Diffusion in a Polymer Network

The transport of nanoparticles (NPs) in polymer networks, as a typical simplified model describing various structures in living systems, is profoundly important in biomedical engineering and nanotechnology. Predicting the effective diffusivity of an NP confined in an ordered network has been an intriguing focus in this frontier field. In the present study, the diffusion of NPs in an unentangled polymer network for different NP radii and network stiffnesses is numerically investigated by single-particle dissipative particle dynamics (DPD). It is found that the deformation due to the junction deviation contributes significantly to the potential barrier U for the NP to overcome during hopping, and it is dominant over the strain energy induced by loop stretching for larger NPs and lower network rigidity. Analyses based on the theory of continuum mechanics reveal that the relation between this deformed energy and the junction deviation can be described by a nonlinear spring. Taking into account the effects of both loop stretching and junction deviation, a double-spring model is proposed to characterize the diffusivity of the NPs in the ordered network. The theoretical prediction is in good agreement with our numerical simulations and qualitatively consistent with previous theoretical studies. This model is helpful to improve our understanding of the dynamic behavior of nanoparticles in a complex biological environment and provide theoretical guidance in designing biomedical applications.

Automated summary

This study numerically investigates the diffusion of nanoparticles in an unentangled polymer network using single-particle dissipative particle dynamics (DPD). The results show that the deformation due to junction deviation significantly affects the diffusion of nanoparticles. Based on the theory of continuum mechanics, a nonlinear spring is proposed to describe the relationship between the deformed energy and the junction deviation. A double-spring model is suggested to characterize the diffusivity of nanoparticles in the ordered network, taking into account both loop stretching and junction deviation effects. The theoretical prediction is in good agreement with numerical simulations and previous theoretical studies.