On the structure and thermodynamics of polymer brushes

The thermodynamic properties of polymeric molecules where one end of the chain is attached to a surface or interface have been investigated. A self-consistent field (SCF) theory has been derived from the (grand) canonical partition function for various situations. The SCF equations were solved numerically within the mean field approximation. The first system comprises a single type of polymer where the segments are can become ionized in an equilibrium chemical reaction with the solvent. The thickness or height of the grafted polymeric layer was studied as a function of the density of grafted chains. The height was generally found to increase with grafting density for chains of intermediate length due to increased osmotic stress caused by the finite volume of the polymer segments. The second situation considered polymers containing a fixed number of charge segments mixed with polymers that contain no charges. The miscibility of these two species was found to be increased when the electrostatic energy of the charged chains was increased due to an increase in the fraction of charged segments or an increase in the electrostatic screening length (reduction in the solution small mobile ion concentration due to added salt). An increase in the density of grafted chains was found to induce instability in the layer if the two polymer species were sufficiently incompatible. In addition, an experimental model system has been developed to observe the stability of such systems. An amphiphilic diblock copolymer of poly(n-butyl acrylate) (PnBA) and poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) was synthesized via atom transfer radical polymerization (ATRP). The hydrophobic PnBA anchoring block was found to be in a near ideal Gaussian conformation on the water surface. This layer collapsed to form a uniform monolayer that nucleated into small domains of bulk polymer at high surface pressures. The stability of the water soluble PDMAEMA layer was observed at low and high salt concentrations by atomic force microscope (AFM) imaging of the polymer layer transferred to graphite substrates via Langmuir-Blodgett (LB) deposition. The AFM images revealed a highly heterogeneous layer when the solution had zero added salt. This is interpreted as a thermodynamically unstable layer. Upon increasing the NaCl concentration to 100 mM the polymer layer was observed to become highly uniform indicating stability