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By use of a combined experimental and theoretical approach, a model poly(ethylene oxide) (PEO) brush system, prepared by spreading a poly(ethylene oxide)-poly(n-butyl acrylate) (PEO-PnBA) amphiphilic diblock copolymer onto an air-water interface, was investigated. The polymer segment density profiles of the PEO brush in the direction normal to the air-water interface under various grafting density conditions were determined by using the neutron reflectivity (NR) measurement technique. To achieve a theoretically sound analysis of the reflectivity data, we used a data analysis method that utilizes the self-consistent field (SCF) theoretical modeling as a tool for predicting expected reflectivity results for comparison with the experimental data. Using this data analysis technique, we discovered that the effective Flory-Huggins interaction parameter of the PEO brush chains is significantly greater than that corresponding to the θ condition in Flory-Huggins solutions (i.e., χ(PEO-water)(brush chains)/χ(PEO-water)(θ condition) ≈ 1.2), suggesting that contrary to what is more commonly observed for PEO in normal situations (χ(PEO-water)(free chains)/χ(PEO-water)(θ condition) ≈ 0.92), the PEO chains are actually not "hydrophilic" when they exist as polymer brush chains, because of the many body interactions that are forced to be effective in the brush situation. This result is further supported by the fact that the surface pressures of the PEO brush calculated on the basis of the measured χ(PEO-water) value are in close agreement with the experimental surface pressure-area isotherm data. The SCF theoretical analysis of the surface pressure behavior of the PEO brush also suggests that even though the grafted PEO chains experience a poor solvent environment, the PEO brush layer exhibits positive surface pressures, because the hydrophobicity of the PEO brush chains (which favors compression) is insufficient to overcome the opposing effect of the chain conformational entropy (which resists compression).

We investigated, by experiment and theory, the lateral structure of a weak polyelectrolyte brush at various added salt concentrations and chain grafting densities. Model poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) brushes with grafting density gradients were developed for this study by using a novel "Langmuir-Blodgett-deposition-under-compression" (LB\C) method. Fluid AFM images of these brushes indicate that the lateral structure of the brush system is sensitive to both added salt concentration and grafting density. Under low salt conditions, 0-20 mM NaCl, the brush structure shows strong microscopic lateral heterogeneities at high grafting densities; both the width and height of the heterogeneities increase with increasing grafting density but are independent of the salt concentration. As the bulk salt concentration is increased to an intermediate regime, 60-100 mM NaCl, these heterogeneities become smaller in size and number, coexisting with smooth homogeneous regions. At high enough concentrations, 300-500 mM NaCl, the entire surface becomes homogeneous. A simple free energy-based Flory-type argument is presented which explains the essential features of the thermodynamic behavior of the brush system. In the zero-salt limit, relatively few monomers are charged, and the hydrophobicity of the backbone chain drives the collapse/aggregation of the chains. At high salt concentrations, the brush chains become sufficiently charged to overcome the hydrophobic nature of the monomers and stabilize the homogeneous state. However, at intermediate salt concentrations, it is found that the osmotic pressure of the counterions surrounding the charged polymer moieties can be decreased by collapsing the chain structure while simultaneously decreasing the number of charges along the backbone and releasing small ions into the bulk solution. This effect, which we term "osmotic instability", serves to destabilize the homogeneous brush configuration.

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.