(a) The gradient of the interaction potential with the surface as a function of the distance of the central segment to the surface. (b) The gradient of the pair interaction as a function of the distance between the two central segments. —solid lines, —dashed lines.
Volume fraction profile produced in a SCF calculation. , , , the equidensity surface is plotted at . The dimensions of the lattice are units. Surfaces indicate positions of hard wall boundaries.
Distributions of energies of 239 snapshots around median values as estimated on the MC stage (light bars) and calculated on the SCF stage (dark bars). , , .
Polymer concentration profiles normalized by bulk polymer volume fraction. (a) Chain length , bulk concentrations 0.05 (dotted line), 0.022 (dot-dash), 0.011 (dashed line), and dilute solution (solid line). (b) Chain length , bulk concentrations 0.069 (dotted line), 0.033 (dot dash), 0.013 (dashed line), and dilute solution (solid line). The relative error of the data points is estimated (Ref. 15) to be ≈0.3%.
Polymer concentration profiles obtained by the classical SCF (crosses), and the hybrid MC-SCF (diamonds) methods. Bulk concentration , . The lines are the best fit of the form with (dot) and (dash). In panel a the profiles near the surface (small values) are shown, whereas in panel b it is shown how the profile goes to the bulk value for the MC-SCF profile.
Logarithm of depletion layer thickness vs logarithm of bulk polymer concentration. MC-SCF results for chain lengths (squares), (diamonds). Dashed lines are added to guide the eye. Classical SCF results for chain lengths (solid line), (dashed line), and results from Ref. 17 rescaled for (circles). The theoretical slope is indicated.
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