Free Energies of Polymer Brushes with Mobile Anchors in a Good Solvent Calculated with the Expanded Ensemble Method

We explore the free energy of “mobile polymer brushes”: The polymer molecules are not chemically bonded to the particle surface but are rather adsorbed by one end. They can desorb to the equilibrium solution and are able to move laterally along the interface. In a good solvent the prevailing forces in the system (apart from the attraction between the adsorbed anchor and the surface) originate from the entropic repulsion between the individual chains. Here we explore the brushes’ free energy and adsorption equilibrium using Brownian Dynamics in conjunction with Expanded Ensembles Monte Carlo simulations that we adapt making it more suitable for polymer brushes. Expanded Ensembles are employed to calculate the excess chemical potential of a polymer chain as a function of the interfacial lateral density, polymer length, and effective exclusion volume of the segment. The thermodynamic properties are related to the structural features, such as brush height, chain radius of gyration, and the in-plane radial distribution function between the chain anchors. Specific attention is paid to the scaling of the excess chemical potential and brush height with the polymer length and interfacial density as well as its influence on the adsorption equilibrium between interface and the bulk polymer solution.