Confinement free energy of surfaces bearing end-grafted polymers in the mushroom regime and local measurement of the polymer density

End-tethered polymer chains usually adopt mushroomlike structures on the surface when their density is low. The behaviors of these surface-attached hemicoils are described by existing polymer theory. Dolan and Edwards derived the free energy of a single polymer chain confined between two planar surfaces. Their theory was used to approximate the steric interaction free energy, E, of two identical surfaces bearing polymers in the mushroom regime and to compare with experimental data obtained from surface force measurements. However, because of a mislabeled plot in the original paper, experimental force profiles did not seem to fit the free energy approximation satisfactorily. We have correctly relabeled the involved plot and derived a new simple expression for E. In order to verify this expression, we have performed experiments on PEG45 polymers incorporated in lipid bilayers using a surface force apparatus. The measured force profiles are in perfect agreement with the prediction. We show that such measurements can be used to determine the local density of grafted polymer with good precision.