Theoretical descriptions of static properties of polymer brushes are reviewed, with an emphasis on monodisperse macromolecules grafted to planar, cylindrical, or spherical substrates. Blob concepts and resulting scaling relations are outlined, and various versions of the self‐consistent field theory are summarized: the classical approximation and the strong stretching limit, as well as the lattice formulation. The physical justification of various inherent assumptions is discussed, and computer simulation results addressing the test of the validity of these approximations are reviewed. Also, alternative theories, such as the single chain mean field theory and the density functional theory, are briefly mentioned, and the main facts about the models used in the computer simulations are summarized. Both molecular dynamics and Monte Carlo simulations are described, the latter including lattice models and bead‐spring models in the continuum. Also extensions such as brush–brush interactions or nanoparticles inside of brushes as well as the solubility of free chains in brushes are briefly mentioned. Pertinent experimental results, though still somewhat scarce, are mentioned throughout and their consequences on the status of the theoretical understanding of polymer brushes is emphasized. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012

Polymer brushes are formed from flexible linear macromolecules tethered at one chain end to a solid substrate, forming a dense polymeric layer of polymer chains which are more or less stretched in the direction perpendicular to the substrate surface. These systems find interest also due to numerous applications (colloid stabilization, improvement of lubrication properties when the surfaces are exposed to shear, protection of the surface against adsorption of nanoparticles or proteins, etc.), for which often the dynamic non-equilibrium response of these brushes to external perturbation is important. The present review summarizes recent computer simulation studies pertinent to these questions. Polymer brushes exposed to shear due to flow of the solvent or a polymer melt the brush interacts with are discussed, and the friction between two brushes is discussed. Another topic that is emphasized is the interaction of polymer brushes with “nanoinclusions” (i.e., small colloidal particles or linear macromolecules down to oligomers), discussing the absorption or expulsion of these objects, and again the response to shear. The simulations are interpreted in terms of scaling concepts and other phenomenological theories wherever possible, and an outlook to related experiments is given.

We study the dynamics of a single semiflexible chain in solution using computer simulations, where we systematically investigate the effect of excluded volume, chain stiffness, and hydrodynamic interactions. We achieve excellent agreement with previous theoretical considerations, but find that the crossover from the time ${\tau }_{\text{b}}$ , up to which free ballistic motion of the monomers describes the chain dynamics, to the times W^$-$1 or ${\tau }_0$ , where anomalous monomer diffusion described by Rouse-type and Zimm-type models sets in, requires two decades of time. While in the limit of fully flexible chains the visibility of the anomalous diffusion behavior is thus rather restricted, the t^3/4 power law predicted for stiff chains without hydrodynamic interactions is verified. Including hydrodynamics, evidence for the predicted ${\left[t\ln (t)\right]}^{3/4}$ behavior is obtained. Similar good agreement with previous theoretical predictions is found for the decay of the bond autocorrelation functions and the end-to-end vector correlation. Finally, several predictions on the variation of characteristic relaxation times with persistence length describing the chain stiffness are tested.

Theoretical predictions by Parry et al. for wetting phenomena in a wedge geometry are tested by Monte Carlo simulations. Simple cubic $L\times L\times L_y$ Ising lattices with nearest neighbor ferromagnetic exchange and four free $L\times L_y$ surfaces, at which antisymmetric surface fields $\pm H_s$ act, are studied for a wide range of linear dimensions $(4\mathrm{}<~L<~320,30<~L_y<~1000),$ in an attempt to clarify finite size effects on the wedge filling transition in this “double-wedge” geometry. Interpreting the Ising model as a lattice gas, the problem is equivalent to a liquid-gas transition in a pore with quadratic cross section, where two walls favor the liquid and the other two walls favor the gas. For temperatures T below the bulk critical temperature $T_c$ this boundary condition (where periodic boundary conditions are used in the y direction along the wedges) leads to the formation of two domains with oppositely oriented magnetization and separated by an interface. For ${L,L}_y\to \infty$ and T larger than the filling transition temperature $T_f{(H}_s),$ this interface runs from the one wedge where the surface planes with a different sign of the surface field meet (on average) straight to the opposite wedge, so that the average magnetization of the system is zero. For $T<\mathrm{}{T}_f{(H}_s),$ however, this interface is bound either to the wedge where the two surfaces with field $-H_s$ meet (then the total magnetization m of the system is positive) or to the opposite wedge (then $m<\mathrm{}0).\mathrm{}$ The distance $l_0$ of the interface midpoint from the wedges is studied as $\overrightarrow{T}{T}_f{(H}_s)$ from below, as is the corresponding behavior of the magnetization and its moments. We consider the variation of $l_0$ for $T>\mathrm{}{T}_f{(H}_s)$ as a function of a bulk field and find that the associated exponents agree with theoretical predictions. The correlation length ${\xi }_y$ in the y direction along the wedges is also studied, and we find no transition for finite L and $L_y\to \infty .$ For $\overrightarrow{L}\infty$ the prediction $l_0\propto {(H}_{\mathrm{sc}}-H_s{)}^{-1/4}$ is verified, where $H_{\mathrm{sc}}\mathrm{}\left(T\right)\mathrm{}$ is the inverse function of $T_f{(H}_s)$ and ${\xi }_y\propto {(H}_{\mathrm{sc}}-H_s{)}^{-3/4},$ respectively. We also find that m vanishes discontinuously at the filling transition. When the corresponding wetting transition is first order we also obtain a first-order filling transition.

Solutions of semiflexible polymers confined by repulsive planar walls are studied by density functional theory and molecular dynamics simulations, to clarify the competition between the chain alignment favored by the wall and the depletion caused by the monomer-wall repulsion. A coarse-grained bead-spring model with a bond bending potential is studied, varying both the contour length and the persistence length of the polymers, as well as the monomer concentration in the solution (good solvent conditions are assumed throughout, and solvent molecules are not included explicitly). The profiles of monomer density and pressure tensor components near the wall are studied, and the surface tension of the solution is obtained. While the surface tension slightly decreases with chain length for flexible polymers, it clearly increases with chain length for stiff polymers. Thus, at fixed density and fixed chain length, the surface tension also increases with increasing persistence length. Chain ends always are enriched near the wall, but this effect is much larger for stiff polymers than for flexible ones. Also the profiles of the mean square gyration radius components near the wall and the nematic order parameter are studied to clarify the conditions where wall-induced nematic order occurs.