Equilibrium polymers at interfaces: Analytical self-consistent-field theory

An analytical mean-field theory is constructed for equilibrium (or "living") polymers with excluded volume at a surface. Within a mean-field approximation, exact analytical expressions are obtained for the monomer concentration profile at the surface and for the excess amount, both for adsorbing and nonadsorbing surfaces, and for the whole concentration range from the dilute to the marginal regime. A ground-state approximation is not needed. For nonadsorbing polymers there is a depletion layer next to the surface with a thickness that passes through a maximum as a function of the monomer concentration. If the equilibrium polymers adsorb on the surface, their behavior is qualitatively different from that of monodisperse chains. For weak adsorption, the excess amount increases gradually as the adsorption energy increases. At a certain finite value of the adsorption energy (which depends on the average length of the chains in the bulk), the excess amount starts to increases very rapidly by orders of magnitude. For chains without excluded volume the excess amount diverges at this point, whereas for real chains it remains finite. Adsorption isotherms of equilibrium polymers show a similar behavior: a gradual increase at low concentrations, then a very steep increase at some finite concentration, and a plateau at higher concentrations.