Modulation of Nanoparticle Diffusion by Surface Ligand Length and Charge: Analysis with Molecular Dynamics Simulations

Abstract

To help better interpret experimental measurement of nanoparticle size, it is important to understand how their diffusion depends on the physical and chemical features of surface ligands. In this study, explicit solvent molecular dynamics simulations are used to probe the effect of ligand charge and flexibility on the diffusion of small gold nanoparticles. The results suggest that despite a high bare charge (+18 e), cationic nanoparticles studied here have reduced diffusion constants compared to a hydrophobic gold nanoparticle by merely a modest amount. Increasing the ligand length by 10 CH2 units also has a limited impact on the diffusion constant. For the three particles studied here, the difference between estimated hydrodynamic radius and radius of gyration is on the order of one solvent layer (3–5 Å), confirming that the significant discrepancies found in the size of similar nanoparticles by recent transmission electron microscopy and dynamic light scattering measurements were due to aggregation under solution conditions. The limited impact of electrostatic friction on the diffusion of highly charged nanoparticles is found to be due to the strong anticorrelation between electrostatic and van der Waals forces between nanoparticle and environment, supporting the generality of recent observation for proteins by Matyushov and co-workers. Including the first shell of solvent molecules as part of the diffusing particle has a minor impact on the total force autocorrelation function but reduces the disparity in relaxation time between the total force and its electrostatic and van der Waals components.

Enhanced Molecular Diffusivity through Destructive Interference between Electrostatic and Osmotic Forces

“…It is accurate for solvated proteins 4 and dipolar solutes, 5,8 but is not exactly followed for small ions 9 and spherical solutes studied here and for charged nanoparticles studied elsewhere. 7 The reason is an incomplete compensation between the vdW and electrostatic forces, leading to a negative total force in the body frame in eq 1.…”

“…The variance of the total force F = F vdW + F E in the laboratory frame includes a negative cross-correlation ⟨δ F vdW ·δ F E ⟩. If in eq , and the force variance comes as a result of subtraction between self-vdW and electrostatic terms ,, …”

Do Electrostatics Control the Diffusive Dynamics of Solitary Water? NMR and MD Studies of Water Translation and Rotation in Dipolar and Ionic Solvents

“…Computer simulations discussed here and elsewhere − explain the impossibility of analyzing friction on molecules as polar as water in terms of additive hydrodynamic and electrostatic contributions. Strong electrostatic interactions lead to electrostriction , and to anticorrelation between Lennard-Jones and electrostatic forces and torques, rendering the friction originating from these two types of interactions inseparable.…”

“…The importance of such cross-correlations, which defeat simple attempts to decompose friction into hydrodynamic and electrostatic components, was already recognized in early studies, 114−117 and has recently been highlighted in simulations of a variety of solutes in aqueous solution. 118,119 The origin of the coupling between hydrodynamic and electrostatic forces is what we term "electrostriction", the buildup of solvent density near a solute when strong solute− solvent electrostatic interactions are present. 116,119 As seen in Figure 10, in highly polar solvents such interactions result in large negative values of frictional components, rendering the friction on small ions, dipolar solutes, and proteins in water orders of magnitude smaller than would otherwise be expected.…”