Subdiffusion of sticky dendrimers in an associative polymer network

TL;DR

This study probes how dendrimer tracers diffuse through a linear associative polymer network, focusing on how sticky (A–A and B–C) interactions alter dendrimer size, local network structure, and transport. It uses coarse-grained Brownian dynamics with hydrodynamic interactions and a Monte Carlo binding scheme to compare non-sticky and sticky dendrimers across a range of concentrations and sticker strengths, revealing that sticky dendrimers can exhibit subdiffusion even when their size is smaller than the network mesh, due to transient binding and binding lifetime scales. The long-time diffusivity follows a Dell–Schweizer–type scaling with an effective confinement parameter, while the hopping picture of Cai et al. does not capture these soft, flexible, and reversible-binding systems; sticky dendrimers also deform the mesh, broadening the distribution of local pore sizes. Collectively, these results illuminate how macromolecular architecture and transient binding govern transport in crowded polymer networks, with implications for drug delivery, viral diffusion in mucus, and nanoparticle transport in gels.

Abstract

We investigate the static and dynamic properties of dendrimers diffusing through a network of linear associative polymers using coarse-grained Brownian dynamics simulations. Both dendrimers and network chains are modelled as bead-spring chain polymers, with hydrodynamic interactions incorporated for the accurate prediction of dynamic properties. Linear chains form a network via the associating groups distributed along their backbones, and the dendrimers interact attractively or repulsively with the network, enabling a direct comparison of sticky and non-sticky behaviour of dendrimers. Structural analysis reveals that while non-sticky dendrimers shrink with increasing network concentration, similar to linear polymer behaviour, sticky dendrimers exhibit stretching at low concentrations due to binding interactions. Dendrimer dynamics are largely insensitive to network architecture but are strongly influenced by the strength of dendrimer-network interactions. Increasing attraction to the network leads to subdiffusive motion and non-Gaussian displacement statistics, even when dendrimers are smaller than the average mesh size. The long-time diffusivity aligns with theoretical predictions for nanoparticle transport in polymer networks. Additionally, dendrimers deform the network locally, altering the mesh size distribution depending on their stickiness. These findings offer insight into the interplay between macromolecular architecture, binding interactions, and transport in polymeric environments.

Figures (14)

• Figure 1: (Color online) (a) Schematic representation of dendrimers in a network of linear chains. The black and brown beads are the homopolymer beads belonging to the linear chain and dendrimer, respectively. The red, blue and green beads are stickers. (b) A generation two ($g=2$) dendrimer with functionality three ($f=3$) and one spacer bead ($s=1$). The order of dendra ($m=f-1$) is two ($m=2$). Beads corresponding to each generation are arranged in concentric circles. The bead numbering scheme is explained in Section S1 in the Supporting Information.
• Figure 2: Different types of stickers present in the model are shown. The red, blue and green beads are stickers of types A, B and C respectively. The black beads are the homopolymer beads present on the linear chain and the brown beads are those on the dendrimer, respectively.
• Figure 3: The various sticker-related parameters associated with the system of sticky dendrimer in a network.
• Figure 4: A snapshot from simulations of sticky star polymers ($f,s,g,\chi$)=(3,2,0,0.5) in linear associative polymers at $c/c^{\ast}=0.5$. The white and brown beads in the system are the backbone monomers (non-sticky) on the linear chains and dendrimers respectively. The coloured beads are stickers of type A (red), type B (blue) and type C (green). Type A stickers interact with themselves to form a network while types B and C represent the linear chain-dendrimer interaction.
• Figure 5: (a) Effect of the sticker strength and concentration on the normalised radius of gyration of dendrimers. The right pointing and up pointing triangles are non-sticky dendrimers in solution and network respectively. The stars and circles are sticky dendrimers with low sticker strengths, while the diamonds, hexagons, squares and left pointing triangles are for higher sticker strengths. (b) Effect of distance between type B stickers ($s_{\mathrm{d}}$) and concentration on sticky dendrimers with $\epsilon_{\textrm{N}}=8$ and $\epsilon_{\textrm{d}}=4$. For comparison, data for homopolymers in semidilute solutions is also included. Error bars are smaller than the marker size.