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Register a new userDynamics of nanoparticles in polydisperse polymer networks: From free diffusion to hopping
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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.
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In our previous publication (Ref. 1) we have shown that the data for the normalized diffusion coefficient of the polymers, $D_p/D_{p0}$, falls on a master curve when plotted as a function of $h/lambda_d$, where $h$ is the mean interparticle distance and $lambda_d$ is a dynamic length scale. In the present note we show that also the normalized diffusion coefficient of the nanoparticles, $D_N/D_{N0}$, collapses on a master curve when plotted as a function of $h/R_h$, where $R_h$ is the hydrodynamic radius of the nanoparticles.
We have applied recent machine learning advances, deep convolutional neural network, to three-dimensional (voxels) soft matter data, generated by Molecular Dynamics computer simulation. We have focused on the structural and phase properties of a coarse-grained model of hydrated ionic surfactants. We have trained a classifier able to automatically detect the water quantity absorbed in the system, therefore associating to each hydration level the corresponding most representative nano-structure. Based on the notion of transfer learning, we have next applied the same network to the related polymeric ionomer Nafion, and have extracted a measure of the similarity of these configurations with those above. We demonstrate that on this basis it is possible to express the static structure factor of the polymer at fixed hydration level as a superposition of those of the surfactants at multiple water contents. We suggest that such a procedure can provide a useful, agnostic, data-driven, precise description of the multi-scale structure of disordered materials, without resorting to any a-priori model picture.
We examine the dynamics of silica particles grafted with high molecular weight polystyrene suspended in semidilute solutions of chemically similar linear polymer using x-ray photon correlation spectroscopy. The particle dynamics decouple from the bulk viscosity despite their large hydrodynamic size and instead experience an effective viscosity that depends on the molecular weight of the free polymer chains. Unlike for hard sphere nanoparticles in semidilute polymer solutions, the diffusivities of the polymer-grafted nanoparticles do not collapse onto a master curve as a function of normalized length scales. These results suggest that the soft interaction potential between polymer-grafted nanoparticles and free polymer allows polymer-grafted nanoparticles to diffuse faster than predicted based on bulk rheology and modifies the coupling between grafted particle dynamics and the relaxations of the surrounding free polymer.
In order to characterize the geometrical mesh size $xi$, we simulate a solution of coarse-grained polymers with densities ranging from the dilute to the concentrated regime and for different chain lengths. Conventional ways to estimate $xi$ rely either on scaling assumptions which give $xi$ only up to an unknown multiplicative factor, or on measurements of the monomer density fluctuation correlation length $xi_c$. We determine $xi_c$ from the monomer structure factor and from the radial distribution function, and find that the identification $xi=xi_c$ is not justified outside of the semidilute regime. In order to better characterize $xi$, we compute the pore size distribution (PSD) following two different definitions, one by Torquato et al. (Ref.1) and one by Gubbins et al. (Ref.2). We show that the mean values of the two distributions, $langle r rangle_T$ and $langle r rangle_G$, both display the behavior predicted for $xi$ by scaling theory, and argue that $xi$ can be identified with either one of these quantities. This identification allows to interpret the PSD as the distribution of mesh sizes, a quantity which conventional methods cannot access. Finally, we show that it is possible to map a polymer solution on a system of hard or overlapping spheres, for which Torquatos PSD can be computed analytically and reproduces accurately the PSD of the solution. We give an expression that allows $langle r rangle_T$ to be estimated with great accuracy in the semidilute regime by knowing only the radius of gyration and the density of the polymers.
We generalize the force-level, microscopic, Nonlinear Langevin Equation (NLE) theory and its elastically collective generalization (ECNLE theory) of activated dynamics in bulk spherical particle liquids to address the influence of random particle pinning on structural relaxation. The simplest neutral confinement model is analyzed for hard spheres where there is no change of the equilibrium pair structure upon particle pinning. As the pinned fraction grows, cage scale dynamical constraints are intensified in a manner that increases with density. This results in the mobile particles becoming more transiently localized, with increases of the jump distance, cage scale barrier and NLE theory mean hopping time; subtle changes of the dynamic shear modulus are predicted. The results are contrasted with recent simulations. Similarities in relaxation behavior are identified in the dynamic precursor regime, including a roughly exponential, or weakly supra-exponential, growth of the alpha time with pinning fraction and a reduction of dynamic fragility. However, the increase of the alpha time with pinning predicted by the local NLE theory is too small, and severely so at very high volume fractions. The strong deviations are argued to be due to the longer range collective elasticity aspect of the problem which is expected to be modified by random pinning in a complex manner. A qualitative physical scenario is offered for how the three distinct aspects that quantify the elastic barrier may change with pinning. ECNLE theory calculations of the alpha time are then presented based on the simplest effective-medium-like treatment for how random pinning modifies the elastic barrier. The results appear to be consistent with most, but not all, trends seen in recent simulations. Key open problems are discussed with regards to both theory and simulation.
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