Effect of Interfacial Curvature on the Miscibility of Laterally Mobile, Mixed Polyelectrolyte and Neutral Polymer Brushes: An SCF Numerical Analysis

Theoretical Modeling of Chemical Equilibrium in Weak Polyelectrolyte Layers on Curved Nanosystems

Surface functionalization with end-tethered weak polyelectrolytes (PE) is a versatile way to modify and control surface properties, given their ability to alter their degree of charge depending on external cues like pH and salt concentration. Weak PEs find usage in a wide range of applications, from colloidal stabilization, lubrication, adhesion, wetting to biomedical applications such as drug delivery and theranostics applications. They are also ubiquitous in many biological systems. Here, we present an overview of some of the main theoretical methods that we consider key in the field of weak PE at interfaces. Several applications involving engineered nanoparticles, synthetic and biological nanopores, as well as biological macromolecules are discussed to illustrate the salient features of systems involving weak PE near an interface or under (nano)confinement. The key feature is that by confining weak PEs near an interface the degree of charge is different from what would be expected in solution. This is the result of the strong coupling between structural organization of weak PE and its chemical state. The responsiveness of engineered and biological nanomaterials comprising weak PE combined with an adequate level of modeling can provide the keys to a rational design of smart nanosystems.

Numerical study of weak polybase brushes grafted on neutral or charged spherical surface by the self-consistent field theory

The self-consistent field theory (SCFT) is employed to numerically study the response of weak polybase type polymer chains grafted on a sphere to electric fields generated by the uniform positive or negative charges on the grafting substrate in the planar polyelectrolyte brush limit. Also the effect of curvature of the grafting sphere on the brush height of weak polybase brushes in the absence of surface charges is investigated. The numerical study reveals interesting and nontrivial dependence of the brush height on the radius of the grafting substrate. Consistent with experimental results, in the parameter range of the surface charge density examined, the brush height is found to be independent of the applied electric field at intermediate and high grafting densities. At relatively low grafting density, the applied negative surface charge which is termed as negative bias in this study results in a reduction of the brush height. At rather low grafting density, the positive bias corresponding to applied positive surface charges can lead to a slight increase in the brush height. The underlining mechanism governing the response of weak polybase brushes to the applied electric field is elucidated.

Ripple structures of mixed homopolymer brushes grafted on cylindrical surfaces: controlling the orientation of the pattern by attuning the substrate curvatures

We employed the strong segregation theory (SST) to study the phase structures of mixed homopolymer brushes grafted on cylindrical surfaces. We considered a simplified case in which two incompatible homopolymers have the same chain length and grafting density. Under these conditions, micro-phase separation in the brush may result in either ripple or helix structures. By comparing the free energy of the possible candidate structures, we found that the helix structure is never the most stable one, while the stability of the perpendicular and parallel ripple structures are sensitive to the curvature of the grafting substrate. It was found that the morphology orientation of the mixed homopolymer brushes can be controlled by attuning the geometry of the substrates.

Effect of salt on the compression of polyelectrolyte brushes in a theta solvent

Classical strong-stretching theory (SST) predicts that, as opposing polyelectrolyte brushes are compressed together in a salt-free theta solvent, they contract so as to maintain a finite polymer-free gap, which offers a potential explanation for the ultra-low frictional forces observed in experiments despite the application of large normal forces. However, the SST ignores chain fluctuations, which would tend to close the gap resulting in physical contact and in turn significant friction. In a preceding study, we examined the effect of fluctuations using self-consistent field theory (SCFT) and illustrated that high normal forces can still be applied before the gap is destroyed. We now look at the effect of adding salt. It is found to reduce the long-range interaction between the brushes but has little effect on the short-range part, provided the concentration does not enter the salted-brush regime. Consequently, the maximum normal force between two planar brushes at the point of contact is remarkably unaffected by salt. For the crossed-cylinder geometry commonly used in experiments, however, there is a gradual reduction because in this case the long-range part of the interaction contributes to the maximum normal force.

Self-consistent field theory study of the effect of grafting density on the height of a weak polyelectrolyte brush

The height of weakly basic polyelectrolyte brushes in the osmotic brush regime is studied as a function of the grafting density using a numerical self-consistent field theory derived from the (semi)grand canonical partition function. The theory is shown to properly account for the local nature of the charge equilibrium and to capture the basic behaviors of polyelectrolyte brushes. On one hand, we find, in agreement with recent experiments, that the scaling of brush height with grafting density can be qualitatively different at intermediate chain lengths than that predicted by basic scaling arguments. This difference is attributed to the relative strength of electrostatic type interactions compared to finite segment size packing constraints. On the other hand, the trend of decreasing brush height with increasing grafting density predicted by the classic scaling analysis is recovered for large molecular weight polymers immersed in a solution of very weak ionic strength.

Chemical and structural changes in a pH-responsive mixed polyelectrolyte brush studied by infrared ellipsometry

This work provides direct chemical and structural insight into pH-dependent changes of an ultrathin (d=12 nm) mixed polyelectrolyte brush. In-situ infrared spectroscopic ellipsometry was used for the first time to study the gradual pH-responsive behavior of the brush, constituted of weak anionic and cationic polyelectrolytes, poly(acrylic acid) (PAA) and poly(2-vinylpyridine) (P2VP), respectively. The pH-dependent infrared fingerprints in the mid-infrared spectral range were analyzed as a function of chemical and structural changes in the mixed brush caused by pH changes. Thereby, the IR spectra were directly correlated to different chemical states of the brush, giving previously not accessible new information on the ionization of the thin film. In contrast to other techniques (e.g., classical attenuated total reflection IR spectroscopy) we used almost plane Si-substrates for the IR ellipsometric approach with application of a single reflection mode. The optical path through Si is of minimal length, which makes a large spectral range accessible. For the most pronounced bands of the carboxyl group at 1718 cm(-1) and the carboxylate ion at 1565 cm(-1), the band amplitudes were correlated with the degree of ionization of the carboxylic groups. Interpretation of the pH-dependent changes in the spectral signature reveals gradual changes of the chemical structures of the mixed brush between three distinct switchable states: strongly ionized PAA at pH 10, strongly ionized P2VP at pH 2, and mainly nonionized functional groups in a "dry" PAA-P2VP polyelectrolyte complex in the range from pH=4 to pH=7. At intermediate pH, the IR spectra confirm the previously made hypothesis of the formation of a polyelectrolyte complex between P2VP and PAA in the mixed brush. From IR spectra it is also concluded that the polyelectrolyte complex is formed as a result of a small fraction of ionized functional groups.