Polymer brushes in solvents of variable quality: Molecular dynamics simulations using explicit solvent

The structure and thermodynamic properties of a system of end-grafted flexible polymer chains grafted to a flat substrate and exposed to a solvent of variable quality are studied by molecular dynamics methods. The macromolecules are described by a coarse-grained bead-spring model, and the solvent molecules by pointlike particles, assuming Lennard-Jones-type interactions between pairs of monomers (epsilon(pp)), solvent molecules (epsilon(ss)), and solvent monomer (epsilon(ps)), respectively. Varying the grafting density sigma(g) and some of these energy parameters, we obtain density profiles of solvent particles and monomers, study structural properties of the chain (gyration radius componen…

Hydrokinetic simulations of nanoscopic precursor films in rough channels

We report on simulations of capillary filling of high-wetting fluids in nano-channels with and without obstacles. We use atomistic (molecular dynamics) and hydrokinetic (lattice-Boltzmann) approaches which point out clear evidence of the formation of thin precursor films, moving ahead of the main capillary front. The dynamics of the precursor films is found to obey a square-root law as the main capillary front, z^2(t) ~ t, although with a larger prefactor, which we find to take the same value for the different geometries (2D-3D) under inspection. The two methods show a quantitative agreement which indicates that the formation and propagation of thin precursors can be handled at a mesoscopic…

Structure of Polymer Brushes in Cylindrical Tubes: A Molecular Dynamics Simulation

Molecular Dynamics simulations of a coarse-grained bead-spring model of flexible macromolecules tethered with one end to the surface of a cylindrical pore are presented. Chain length $N$ and grafting density $\sigma$ are varied over a wide range and the crossover from ``mushroom'' to ``brush'' behavior is studied for three pore diameters. The monomer density profile and the distribution of the free chain ends are computed and compared to the corresponding model of polymer brushes at flat substrates. It is found that there exists a regime of $N$ and $\sigma$ for large enough pore diameter where the brush height in the pore exceeds the brush height on the flat substrate, while for large enoug…

Molecular dynamics simulations of capillary rise experiments in nanotubes coated with polymer brushes.

The capillary filling of a nanotube coated with a polymer brush is studied by molecular dynamics simulations of a coarse-grained model, assuming various conditions for the fluid-wall and fluid-brush interactions. Whereas the fluid is modeled by simple point particles interacting with Lennard-Jones forces, the (end-grafted, fully flexible) polymers that form the brush coating are described by a standard bead-spring model. Our experiments reveal that capillary filling is observed even for walls that would not be wetted by the fluid, provided the polymer brush coating itself wets. Generally, it is found that the capillary rise always proceeds through a t1/2 law with time t while the underlying…

Capillary Rise in Nanopores: Molecular Dynamics Evidence for the Lucas-Washburn Equation

When a capillary is inserted into a liquid, the liquid will rapidly flow into it. This phenomenon, well studied and understood on the macroscale, is investigated by Molecular Dynamics simulations for coarse-grained models of nanotubes. Both a simple Lennard-Jones fluid and a model for a polymer melt are considered. In both cases after a transient period (of a few nanoseconds) the meniscus rises according to a $\sqrt{\textrm{time}}$-law. For the polymer melt, however, we find that the capillary flow exhibits a slip length $\delta$, comparable in size with the nanotube radius $R$. We show that a consistent description of the imbibition process in nanotubes is only possible upon modification o…

Capillary Rise in Nanotubes Coated with Polymer Brushes

The spontaneous rise of a fluid in a brush-coated nanocapillary is studied by molecular dynamics simulation of a coarse-grained model. The cases of changing wettability of both the capillary walls and the brush were examined. We also investigated the impact of polymer chain length on the transport of fluid along the nanotube. We found that capillary filling takes place in both lyophilic and lyophobic tubes, provided that the polymer brush coating is wetted by the fluid. In all the cases studied, capillary rise proceeds by a time-square law, but the mechanisms behind them (Lucas-Washburn or diffusive propagation) differ, depending on the chain length N. For a wettable wall, the speed of flui…

Excess free energy of nanoparticles in a polymer brush

Abstract We present an efficient method for direct determination of the excess free energy Δ F of a nanoparticle inserted into a polymer brush. In contrast to Widom's insertion method, the present approach can be efficiently implemented by Monte Carlo or Molecular Dynamics methods also in a dense environment. In the present investigation the method is used to determine the free energy penalty Δ F ( R , D ) for placing a spherical particle with an arbitrary radius R at different positions D between the grafting plane and the brush surface. Deep inside the brush, or for dense brushes, one finds Δ F  ∝  R 3 whereas for shallow nanoclusions Δ F  ∝  R 2 , regardless of the particle interaction (…

Polymer Brushes on Flat and Curved Substrates: Scaling Concepts and Computer Simulations

The scaling concepts for isolated flexible macromolecules in good solvent grafted with one chain end to a flat surface (polymer mushrooms) as well as for layers of many overlapping end-grafted chain molecules (polymer brushes) are introduced. Monte Carlo attempts to test these concepts are briefly reviewed. Then the extension of these concepts to polymer brushes grafted to the interior of a cylinder surface is discussed. Molecular Dynamics results on chain average linear dimensions in the direction normal to the grafting surface and in axial direction are described, as well as distribution functions for the density of end monomers and of all monomers of the chains. It is argued that under t…

Cover Picture: Macromol. Theory Simul. 7/2006

Local Viscosity in the Vicinity of a Wall Coated by Polymer Brush from Green-Kubo Relations

When fluids are confined in slit pores between parallel walls, their static structures and their dynamical properties exhibit inhomogeneity in the z-direction perpendicular to the wall. Of particular interest are local bulk viscosity η b (z) and shear viscosity η s (z). Here, we discuss an algorithm to estimate these quantities from Green-Kubo relations using equilibrium molecular dynamics. As an application example, a polymer brush (macromolecules end-grafted to a substrate at z= 0) interacting with a solvent formed from point-like particles is given.

Method for wettability characterization based on contact line pinning.

We demonstrate an efficient and reliable method for wettability characterization by determining the contact angle theta which a liquid-vapor interface makes with a solid wall. The purpose is to overcome the difficulties, related to the curvature of the liquid-vapor interface, which make measurements of theta rather uncertain, especially on the micro- and nanoscale. The method employs a specially designed slitlike channel in contact with a reservoir whereby the wettability of one of the slit walls is to be examined whereas the other (auxiliary) wall is separated by half into a lyophilic and a lyophobic part so as to pin the incoming fluid and fix the one end of the liquid-vapor interface. In…