Loop statistics in adsorbed polymer solutions

Abstract

Classical theories of polymer adsorption describe adsorbed polymer chains in terms of tails, trains and loops [ 11. The trains are segments of consecutive monomers directly in contact with the adsorbing surface. In between two trains the chain forms loops; the end sections between the last train and the end points are the tails. This description has been refined and made more quantitative in the numerical studies initiated in Wageningen by Scheutjens and Fleer [2]. An alternative way to study polymer adsorption from solution is to follow Edwards’ [ 31 description of semi-dilute polymer solutions and to characterize the solution locally by the order parameter $(r) related to the local concentration by c(r) = $(r)*. In this approach, the chains are considered as infinite and the only relevant variable is the monomer concentration that decreases from the wall towards an imposed bulk value. This approach has been extended by de Gennes [4] who introduced scaling laws to take into account the local excluded volume correlations. He also proposed a self-similar construction for the concentration profile that seems to agree with many experimental results. Our aim here is to try and bridge the gap between the two approaches and to show how the Edwards self-consistent approach allows the determination of single chain properties such as the