The behaviour of an ideal polymer chain interacting with two parallel surfaces

The behaviour of a long isolated ideal chain polymer interacting with two parallel surfaces is investigated within the context of a simple cubic lattice model in three dimensions. In order to be able to obtain information about the contacts of the polymer with the plates the full chain is subdivided into trains, loops and bridges. A maximum term method is used to calculate the configuration sum of the polymer. In order to find the distribution of the subchains that maximises the partition function in the limit of infinite molecular weight a Lagrange multiplier method has been applied. This gives a closed set of equations from which one can uniquely calculate all relevant thermodynamic quantities as a function of the interaction energy, the temperature and the distance between the plates. In addition to the free energy and the entropy of the chain also the fraction of monomers on the surface and the number of trains is calculated. Next we give results about the ratio between the number of bridges and loops and the fraction of monomers in these loops and bridges. Finally the effective force between the plates due to the polymer material is calculated. The results for large plate separation are compared with those of the single plate.