Universal Relation for Effective Interaction between Polymer-Grafted Nanoparticles

Abstract

Understanding the interactions between polymer-grafted nanoparticles is imperative to predict the macroscale mechanical properties of the nanocomposites they form. Molecular dynamics simulations capture the interfacial effects of grafting on structure and mobility, but directly linking these features to macroscale constitutive relations for nanocomposites remains challenging. As a step toward addressing this challenge, we develop a computational framework to predict the effective pairwise interparticle interactions between polymer-grafted nanoparticles with different design parameters, that is, polymer chain length, grafting density, and polymer chemistry. Using coarse-grained molecular dynamics simulations, we evaluate the potential of mean force between two nanoparticles by varying their radial distance under uniaxial deformations, from which an effective interaction can be derived. We find that the repulsive part of the interaction can be expressed as an exponential repulsion term, whereas the attractive part is best captured using a sigmoidal form. The empirical constants of these equations depend linearly on the chain length and quadratically on the grafting density. To ensure that the finite rate of deformation does not affect our conclusions, we also take into account the strain rate dependence of the effective interaction, using a Cowper–Symonds model to extrapolate the zero-rate limit of our results. With the development of this interatomic potential between the nanoparticles, we propose a mesoscopic model for nanoparticle assemblies that circumvents the need to explicitly simulate polymer chains, significantly improving the computational efficiency by extending the spatiotemporal scales by 6–7 orders of magnitude.

Solvation Free Energy of Dilute Grafted (Nano)Particles in Polymer Melts via the Self-Consistent Field Theory

“…As a result, we can explicitly predict the evolution of the polymer affinity to the solid surface (zero, low, high, and perfect wetting) with increasing curvature. We demonstrate that the behavior of the system is quite different when addressing planar and spherical interfaces ,− and compare the overall behavior against theoretical − and experimental , observations.…”

“…According to Praetorius et al, knowing the solvation free energies and the corresponding partition coefficient is only one part of the problem. In addition, one also needs information on other thermodynamic aspects of the system, namely, the free energy of solid/liquid , and liquid/liquid − interphases and the potential of mean force, ,− , which is directly related to the aggregation tendencies of the NPs. Through this information, one can obtain a broader picture regarding the thermodynamics and evolution of a composite system.…”

Polymer‐Grafted Nanoparticles (PGNs) with Adjustable Graft‐Density and Interparticle Hydrogen Bonding Interaction

“…Whereas the self‐assembly of polymeric colloid micro‐and nanoparticles is well studied, [ 26 ] the formation of 2D and 3D superlattice structures of PGNs is affected by factors such as the nanoparticle size, graft density, the molar mass of the grafted chains as well as the properties and interparticle interactions of the polymer chains. [ 27 ]…”

Internal Microstructure Dictates Interactions of Polymer-grafted Nanoparticles in Solution

“…This is consistent with the ratio R cross /R m of Table S1 and can be explained as the shell being less dense and occupying a larger volume with respect to the other samples. Based on the Daoud−Cotton model, 58 this would result in a larger blob size and stronger excluded volume interactions. Therefore, under the same conditions (solvent, temperature), there is a competition between the attractive Van der Waals forces and the repulsive steric effects, which influences the second virial coefficient.…”

“…The core radius is constant R c = 57 ± 4 nm, and the grafting densities range from 0.08 to 0.61 chains/nm 2 while N is in the range 130–2700. Specifically, GNPs of low grafting density (0.1 < σ < 0.3 nm –2 ) with longer chains are expected to exhibit softer behavior characterized by a broader-ranged pair correlation function and pronounced liquid-like ordering compared to hard-sphere suspensions, and this is true both for GNP suspensions and GNP melts (self-suspended). − To determine the effect of graft composition (number and size of grafted chains) on the interactions between particles in solvents, we utilize combined static and dynamic light scattering in conjunction with full form factor analysis to determine the second virial coefficient ( A 2 ) and the translational diffusion coefficient of model GNPs in an athermal solvent for PS. From A 2 , the pair interaction potential is determined and compared to a brush potential derived for grafted spheres in solution.…”