Prediction of energy of interaction among tethered polymer chains confined between two parallel plates

A mean field continuum model has been used to predict the free energy of interaction between the layers of polymer chains grafted on two plane parallel plates. Four cases are considered: (a) a single plate with tethered chains, (b) two plates with equal amount of tethered chains on both plates, (c) tethering only on one plate, the other plate being bare, and (d) tethered loops on two plates. The predicted force-distance profiles are compared with the experimental data, reported in the literature, on interaction of polystyrene chains grafted on mica surface, with toluene as the solvent. The tethered amount is estimated from the regression of the experimental data. The predicted and the experimental profiles are in good agreement except for the case of short tethered loops. Moreover, in the experiment where the tethered amount is reported, the regression estimate closely matches with the actual value. In the cases where the tethered amount is not reported, the estimates of the same show the correct trend. Moreover, the estimated critical distance between the plates at which the tethered layers begin to interact also matches with the experimentally measured values. The present continuum model correctly accounts for the stiffness of the polymer chain and the difference in the size of the Kuhn segment and the solvent molecule. The predictions of the present theory are compared with those of the SCF lattice model of Scheutjens and Fleer