Going beyond mean field theory we develop a model of a polymer brush that allows for inhomogeneity, confinement and lateral interactions. The model is developed for freely rotating chains and a realistic Interacting Chain Model for poly(ethylene glycol). The parameters in the latter are obtained from a first principles theory based on (i) ab initio (density functional theory) calculations of the potential energy surfaces of the polymer conformers, and (2) the proper statistical mechanics for which we succeeded to formulate and solve a Green's function approach (transfer matrix method) in the presence of an external force field. We set up kinetic equations for the time evolution of the growth of a brush from solution. For PEG a detailed analysis and discussion of recent data is made that identifies two time regimes of pancake adsorption and collision-induced conformational conversion to stretched moeities, respectively. Lastly we discuss the possibility that auto-ionization of water in contact with the brush may lead to preferential adsorption of hydroxide and hydronium ions depending on the pH. @FootnoteText@ H.J. Kreuzer, R.L.C. Wang, and M. Grunze, New Journal of Physics 1, 21.1 (1999). R.L.C. Wang, H.J. Kreuzer, and M. Grunze, Phys. Chem. Chem. Phys. 2, 3613 (2000). L. Livadaru, H.J. Kreuzer, and R.R. Netz. Interacting Chain Model for Poly(ethylene glycol) from First Principles. Macromolecules (in press). Kreuzer, H.J.; Payne, S.H.; Livadaru, L. Biophysical Journal 2001, 80(6), 2505-2514. Kreuzer, H.J.; Grunze, M. Europhys. Lett. 2001, 55(5), 640-646. M. Himmelhaus, T. Bastuck, S. Tokuitsu, M. Grunze, L. Livadaru and H.J. Kreuzer. Growth of a polymer brush from solution, (preprint).