Interactions between Sterically Stabilized Nanoparticles: The Effects of Brush Bidispersity and Chain Stiffness

Abstract

Density Functional Theory is employed to study structural properties and interactions between solvent-free polymer-grafted nanoparticles. Both monodisperse and bidisperse polymer brushes with variable chain stiffness are considered. The three major control parameters are the grafting density, the grafted chain length, and its stiffness. The effect of these parameters on the brush-brush overlap and attractive interaction strength is analyzed. The Density Functional Theory results are compared with the available simulation data, and good quantitative agreement is found.

Linear and Ring Polymer Brushes: A Density Functional Theory Study

“…In view of the above discussion of advantages and disadvantages of simulation and mean-field theoretical approaches, it is important to mention that monomer-resolved DFT has been recently tested against extensive MD simulation data for linear brushes [44] and good agreement was found. [45] Likewise, good agreement between MD and DFT results was demonstrated for non-grafted ring and linear chains under planar confinement. [42,43] Finally, lattice-based SCF study of grafted rings [41] produced the same trends in terms of brush microstructural properties and brush-brush interactions as the dissipative particle dynamics simulations.…”

“…For the linear polymer brushes, we employ a microscopic model that was used in a recent DFT study, [45] where a detailed comparison between DFT and MD [44] results has been presented. Specifically, a linear polymer brush is modeled as a flat structureless wall (located in xy-plane), which is grafted uniformly with flexible (no bond-bending potential) polymer chains of length N at grafting density 𝜎 g .…”

“…Substitution of 𝜌 p (R p ) into Equation ( 9) then yields an integral equation for the monomer density distribution 𝜌(r) which needs to be solved numerically. [45] Given that the main focus of the present work is on the brushbrush PMF, we primarily consider two opposing interacting polymer brushes tethered to the parallel flat walls located at z g1 and z g2 , respectively. In this geometry, the equilibrium monomer density distribution 𝜌(z) is a function of a single variable z.…”

“…In this geometry, the equilibrium monomer density distribution 𝜌(z) is a function of a single variable z. [45] The PMF between the two brushes W(z) is obtained as a function of the distance between the walls by taking the difference between the free energy F at the wall separation z and at the wall separation z max = 2N, where the two bushes no longer overlap. [25] The value z = H where W(z) passes through a minimum (W(z = H) = W min ) corresponds to the equilibrium separation between the two walls.…”

“…In addition to the location and depth of the brush-brush PMF, we also study the geometrical parameters that quantify the amount of overlap between two opposing brushes. First, following the MD simulation study [44] and the earlier DFT work, [45] we define the overlap parameter P between the two brushes at the equilibrium separation as follows: Dashed lines: end-monomer distribution N𝜌 e (z) and mid-monomer distribution N𝜌 m (z) for linear and ring brushes, respectively (scaled by the respective chain length N). b) Upper panel: Total monomer density profiles 𝜌 1 (z) and 𝜌 2 (z) for two opposing linear brushes with chain length N = 32, grafting density 𝜎 g = 0.06 at T = 2.…”