[Paper Review] Dynamics of nanoparticles in polydisperse polymer networks: From free diffusion to hopping

Valerio Sorichetti, Virginie Hugouvieux+1 more|arXiv (Cornell University)|Jun 23, 2021

Material Dynamics and Properties102 references51 citations

TL;DR

This study uses molecular dynamics simulations to investigate nanoparticle (NP) diffusion in disordered, polydisperse polymer networks, identifying three dynamical regimes based on the confinement parameter C = σN/λ: free diffusion (C ≲ 1), activated hopping (C ≳ 1), and extreme trapping with quasi-plateaus in mean squared displacement (C ≳ 3). The key contribution is the first simulation evidence of strong dynamical heterogeneity and cage effects in the extreme confinement regime, which neither classical theories nor simulations to date have fully captured.

ABSTRACT

Using molecular dynamics simulations we study the static and dynamic properties of spherical nanoparticles (NPs) embedded in a disordered and polydisperse polymer network. Purely repulsive (RNP) as well as weakly attractive (ANP) polymer-NP interactions are considered. It is found that for both types of particles the NP dynamics at intermediate and at long times is controlled by the confinement parameter $C=\sigma_N/\lambda$, where $\sigma_N$ is the NP diameter and $\lambda$ is the dynamic localization length of the crosslinks. Three dynamical regimes are identified: i) For weak confinement ($C \lesssim 1$) the NPs can freely diffuse through the mesh; ii) For strong confinement ($C \gtrsim 1$) NPs proceed by means of activated hopping; iii) For extreme confinement ($C \gtrsim 3$) the mean squared displacement shows on intermediate time scales a quasi-plateau since the NPs are trapped by the mesh for very long times. Escaping from this local cage is a process that depends strongly on the local environment, thus giving rise to an extremely heterogeneous relaxation dynamics. The simulation data are compared with the two main theories for the diffusion process of NPs in gels. Both theories give a very good description of the $C-$dependence of the NP diffusion constant, but fail to reproduce the heterogeneous dynamics at intermediate time scales.

Motivation & Objective

• To understand the dynamics of spherical nanoparticles (NPs) in disordered, polydisperse, permanently crosslinked polymer networks, a realistic model of real-world gels and rubbers.
• To investigate how NP diffusion transitions from free diffusion to hopping as confinement increases, particularly in the previously unexplored strong confinement regime (C ≳ 3).
• To assess the validity of existing theoretical models for NP diffusion in gels by comparing simulation data with predictions from two major theories.
• To quantify the role of structural heterogeneity in inducing non-Gaussian, non-exponential relaxation dynamics at intermediate timescales.

Proposed method

• Molecular dynamics (MD) simulations of spherical NPs embedded in a disordered, polydisperse polymer network generated via self-assembly of patchy particles with controlled crosslink density.
• The network is formed by bivalent monomers and trivalent crosslinks, with bonds formed until a percolating network is achieved; dangling ends are recursively removed to ensure a fully bonded, stable network.
• The confinement parameter C = σN/λ is used as the central control variable, where σN is the NP diameter and λ is the dynamic localization length of crosslinks.
• Key observables include the mean squared displacement (MSD), van Hove function, non-Gaussian parameter α2(t), and apparent subdiffusive exponent β(t) to characterize diffusion regimes.
• Two interaction types are simulated: purely repulsive (RNP) and weakly attractive (ANP) polymer-NP interactions.
• The simulations probe a wide range of C values up to C ≈ 4, covering the previously inaccessible extreme confinement regime.

Experimental results

Research questions

• RQ1 How does NP diffusion in polydisperse, disordered polymer networks evolve with increasing confinement, as quantified by C = σN/λ?
• RQ2 What dynamical regimes emerge at intermediate and long times, and how do they depend on C, particularly in the strong confinement regime (C > 3)?
• RQ3 To what extent do existing theoretical models for NP diffusion in gels accurately describe the simulated C-dependence of the diffusion coefficient?
• RQ4 Why do simulations show strong dynamical heterogeneity and non-Gaussian behavior at intermediate times, and how does this challenge existing theories?

Key findings

• For C ≲ 1, NPs exhibit free diffusion with MSD scaling linearly with time, indicating unimpeded motion through the network mesh.
• For C ≳ 1, NP dynamics shift to activated hopping, where motion occurs via thermally activated escape from transient cages formed by the mesh.
• For C ≳ 3, the mean squared displacement shows a long-lived quasi-plateau due to extreme trapping, indicating that NPs are confined for very long times.
• The non-Gaussian parameter α2(t) increases with density and C, indicating pronounced dynamical heterogeneity, with escape times from the local cage broadly distributed.
• The apparent subdiffusive exponent β(t) shows a slow transition from subdiffusive to diffusive behavior, with no clear plateau at β = 0, confirming the absence of a true cage effect in the traditional sense.
• Both major theoretical models for NP diffusion in gels accurately predict the C-dependence of the diffusion coefficient but fail to reproduce the observed dynamical heterogeneity and non-Gaussian relaxation at intermediate times.