^{1}, Pawel Keblinski

^{1}and Sanat K. Kumar

^{2}

### Abstract

Molecular dynamics simulations on the Kremer–Grest bead-spring model of polymer melts are used to study the effect of spherical nanoparticles on chain diffusion. We find that chain diffusivity is enhanced relative to its bulk value when polymer-particle interactions are repulsive and is reduced when polymer-particle interactions are strongly attractive. In both cases chain diffusivity assumes its bulk value when the chain center of mass is about one radius of gyration away from the particle surface. This behavior echoes the behavior of polymer melts confined between two flat surfaces, except in the limit of severe confinement where the surface influence on polymer mobility is more pronounced for flat surfaces. A particularly interesting fact is that, even though chain motion is strongly speeded up in the presence of repulsive boundaries, this effect can be reversed by pinning one isolated monomer onto the surface. This result strongly stresses the importance of properly specifying boundary conditions when the near surface dynamics of chains are studied.

The authors acknowledge the financial support of the Office of Naval Research, Contract No. N00014-01-10732, the National Science Foundation through Grant Nos. CMS-0310596 and DMR-0413755, and The National Science Foundation Nanoscale Science and Engineering Center at RPI, NSF Grant No. DMR-0117792. They thank Professor Sandy Sternstein for many useful discussions.

I. INTRODUCTION

II. SIMULATION MODEL AND PROCEDURE

III. RESULTS

A. Nanoparticle-polymer system

1. Chain structure

2. Chain diffusion in the presence of isolated filler

3. Particle concentration effects on chain transport

4. Particle transport

B. Thin films

IV. CONCLUSIONS

### Key Topics

- Polymers
- 62.0
- Nanoparticles
- 39.0
- Diffusion
- 32.0
- Polymer melts
- 15.0
- Surface dynamics
- 11.0

## Figures

Schematic representation of the interactions between a chain monomer and a nanoparticle. The interactions are divided into two parts, the outer 2D shell and inner 3D bulk.

Schematic representation of the interactions between a chain monomer and a nanoparticle. The interactions are divided into two parts, the outer 2D shell and inner 3D bulk.

(a) The particle-monomer radial distribution function as a function of radial distance for repulsive, attractive, and strongly attractive system, respectively. Molecular layering is observed in all cases, and is most pronounced for the strongly attractive system. (b) The potential of mean force as a function of for repulsive, attractive, and strongly attractive systems. The potential barrier for movement between first and second shells is significantly larger than the thermal energy for strongly attractive systems.

(a) The particle-monomer radial distribution function as a function of radial distance for repulsive, attractive, and strongly attractive system, respectively. Molecular layering is observed in all cases, and is most pronounced for the strongly attractive system. (b) The potential of mean force as a function of for repulsive, attractive, and strongly attractive systems. The potential barrier for movement between first and second shells is significantly larger than the thermal energy for strongly attractive systems.

Center of mass diffusion , averaged over all chains, as a function of time for the neat polymer (bulk) and for nanofilled systems. The long-time slope of this graph gives us the diffusion coefficient . The value of is highest for the repulsive nanoparticles, followed successively by the melt and the strongly attractive particle system.

Center of mass diffusion , averaged over all chains, as a function of time for the neat polymer (bulk) and for nanofilled systems. The long-time slope of this graph gives us the diffusion coefficient . The value of is highest for the repulsive nanoparticles, followed successively by the melt and the strongly attractive particle system.

The local diffusion coefficient , normalized to the bulk value, as a function of . For the repulsive particle the diffusion coefficient is highest at the surface. It gradually decreases to the bulk value. Similarly, the diffusion coefficient near the surface is lowest for strongly attractive particle indicating that the chains are less mobile. In both cases the bulk value is recovered away from the particle surface.

The local diffusion coefficient , normalized to the bulk value, as a function of . For the repulsive particle the diffusion coefficient is highest at the surface. It gradually decreases to the bulk value. Similarly, the diffusion coefficient near the surface is lowest for strongly attractive particle indicating that the chains are less mobile. In both cases the bulk value is recovered away from the particle surface.

The normalized overall diffusion coefficient as a function of volume fraction of nanoparticles for the repulsive and the strongly attractive system.

The normalized overall diffusion coefficient as a function of volume fraction of nanoparticles for the repulsive and the strongly attractive system.

The normalized diffusion coefficient as a function of distance from a flat surface for repulsive and attractive surfaces. The first shell, nearest to the surface, has a width of , while all other shells have a width of .

The normalized diffusion coefficient as a function of distance from a flat surface for repulsive and attractive surfaces. The first shell, nearest to the surface, has a width of , while all other shells have a width of .

The same as Fig. 6, but only for strongly attractive flat surfaces for various surface-to-surface distances. For the system in which surfaces are separated at a distance of 8 all the chains are immobilized due to confinement. The widths of the sampling shells for a plate separation of 24 is the same as for Fig. 6. For a plate separation of 16, the first shell has a width of , and the rest are in thickness. For systems of thickness 8, the first and second shells are in width and the third is .

The same as Fig. 6, but only for strongly attractive flat surfaces for various surface-to-surface distances. For the system in which surfaces are separated at a distance of 8 all the chains are immobilized due to confinement. The widths of the sampling shells for a plate separation of 24 is the same as for Fig. 6. For a plate separation of 16, the first shell has a width of , and the rest are in thickness. For systems of thickness 8, the first and second shells are in width and the third is .

(a) Comparing the particle-monomer radial distribution function for nanoparticle and flat surface systems. Both cases correspond to strongly attractive surface polymer interactions. In the case of the flat plate the monomer distribution function is defined as a function of distance normal to the plates. Molecular layering is more pronounced for flat surfaces. The flat surface data are shifted by for better visualization. (b) Comparison of the potential of mean force as a function of radial distance for these two cases. The potential barrier for movement between the first and the second shells is almost three times larger for the flat surfaces.

(a) Comparing the particle-monomer radial distribution function for nanoparticle and flat surface systems. Both cases correspond to strongly attractive surface polymer interactions. In the case of the flat plate the monomer distribution function is defined as a function of distance normal to the plates. Molecular layering is more pronounced for flat surfaces. The flat surface data are shifted by for better visualization. (b) Comparison of the potential of mean force as a function of radial distance for these two cases. The potential barrier for movement between the first and the second shells is almost three times larger for the flat surfaces.

The normalized diffusion coefficient as a function of distance from the plate surface for grafted polymeric chains and grafted monomers, respectively. The surfaces are repulsive to all monomers. The enhanced mobility due to repulsive interaction between plates and the chains near surface is reduced in both cases, with the effect being more pronounced for grafted chains. All shells are of a width .

The normalized diffusion coefficient as a function of distance from the plate surface for grafted polymeric chains and grafted monomers, respectively. The surfaces are repulsive to all monomers. The enhanced mobility due to repulsive interaction between plates and the chains near surface is reduced in both cases, with the effect being more pronounced for grafted chains. All shells are of a width .

## Tables

Comparison of radius of gyration for systems with and without repulsive nanoparticles for different chain lengths at 2.5% volume fraction of nanoparticles.

Comparison of radius of gyration for systems with and without repulsive nanoparticles for different chain lengths at 2.5% volume fraction of nanoparticles.

Comparison of the radius of gyration for systems containing repulsive and strongly attractive nanoparticles for different chain lengths at 5% and 10% volume fraction of nanoparticles. There was no appreciable change found in the radius of gyration of polymer chains even at high nanoparticle concentration.

Comparison of the radius of gyration for systems containing repulsive and strongly attractive nanoparticles for different chain lengths at 5% and 10% volume fraction of nanoparticles. There was no appreciable change found in the radius of gyration of polymer chains even at high nanoparticle concentration.

The diffusion coefficient of chains and the nanoparticle for strongly attractive nanoparticle and repulsive nanoparticle systems containing heavy, light, and stationary nanoparticles.

The diffusion coefficient of chains and the nanoparticle for strongly attractive nanoparticle and repulsive nanoparticle systems containing heavy, light, and stationary nanoparticles.

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