The interaction of colloidal particles with a planar polymer brush immersed in a solvent of variable thermodynamic quality is studied by a numerical self-consistent field method combined with analytical mean-field theory.

Weak polyampholytes and globular proteins among them can be efficiently absorbed from solutions by polyelectrolyte brushes or microgels even if the net charge of the polyampholyte is of the same sign as that of the brush/microgel. We use a mean-field approach for calculating the free energy of insertion of a probe polyampholyte molecule into a polyelectrolyte brush/microgel. We anticipate that the insertion of the polyampholyte into similarly charged brush/microgel may be thermodynamically favorable due to the gain in the cumulative re-ionization free energy of the pH-sensitive acidic and basic residues. Importantly, we demonstrate that the polyampholyte (protein) charge sign inversion upon transfer from the bulk of the solution to the brush/microgel does not provide sufficient conditions to assure negative re-ionization free energy balance. Thus (in the absence of other driving or stopping mechanisms), charge sign inversion does not necessarily provoke spontaneous absorption of the polyampholyte into the brush/microgel.

The self-consistent field Poisson–Boltzmann framework is applied to analyze equilibrium partitioning of ampholytic nanoparticles (NPs) between buffer solution and polyelectrolyte (PE) polyanionic brush. We demonstrate that depending on pH and salt concentration in the buffer solution, interactions between ionizable (acidic and basic) groups on the NP surface and electrostatic field created by PE brush may either lead to the spontaneous uptake of NPs or create an electrostatic potential barrier, preventing the penetration of NPs inside PE brush. The capability of PE brush to absorb or repel NPs is determined by the shape of the insertion free energy that is calculated as a function of NP distance from the grafting surface. It is demonstrated that, at a pH value below or slightly above the isoelectric point (IEP), the electrostatic free energy of the particle is negative inside the brush and absorption is thermodynamically favorable. In the latter case, the insertion free energy exhibits a local maximum (potential barrier) at the entrance to the brush. An increase in pH leads to the shallowing of the free energy minimum inside the brush and a concomitant increase in the free energy maximum, which may result in kinetic hindering of NP uptake. Upon further increase in pH the insertion free energy becomes positive, making NP absorption thermodynamically unfavorable. An increase in salt concentration diminishes the depth of the free energy minimum inside the brush and eventually leads to its disappearance. Hence, in accordance with existing experimental data our theory predicts that an increase in salt concentration suppresses absorption of NPs (protein globules) by PE brush in the vicinity of IEP. The interplay between electrostatic driving force for NP absorption and osmotic repelling force (proportional to NP volume) indicates that for large NPs with relatively small number of ionizable groups osmotic repulsion overcomes electrostatic attraction preventing thereby absorption of NPs by PE brush.

To study conformational transition occuring upon inferior solvent strength in a brush formed by linear or dendritically branched macromolecules tethered to the inner surface of cylindrical or planar (slit-like) pore, a self-consistent field analytical approach is employed. Variations in the internal brush structure as a function of variable solvent strength and pore radius, and the onset of formation of a hollow channel in the pore center are analysed. The predictions of analytical theory are supported and complemented by numerical modelling by a self-consistent field Scheutjens–Fleer method. Scaling arguments are used to study microphase segregation under poor solvent conditions leading to formation of a laterally and longitudinally patterned structure in planar and cylindrical pores, respectively, and the effects of confinement on "octopus-like" clusters in the pores of different geometries.

Polymer brushes are attractive as surface coatings for a wide range of applications, from fundamental research to everyday life, and also play important roles in biological systems. How colloids (e.g., functional nanoparticles, proteins, viruses) bind and move across polymer brushes is an important yet under‐studied problem. A mean‐field theoretical approach is presented to analyze the binding and transport of colloids in planar polymer brushes. The theory explicitly considers the effect of solvent strength on brush conformation and of colloid‐polymer affinity on colloid binding and transport. The position‐dependent free energy of the colloid insertion into the polymer brush which controls the rate of colloid transport across the brush is derived. It is shown how the properties of the brush can be adjusted for brushes to be highly selective, effectively serving as tuneable gates with respect to colloid size and affinity to the brush‐forming polymer. The most important parameter regime simultaneously allowing for high brush permeability and selectivity corresponds to a condition when the repulsive and attractive contributions to the colloid insertion free energy nearly cancel. This theory should be useful to design sensing and purification devices with enhanced selectivity and to better understand mechanisms underpinning the functions of biological polymer brushes.