A polymer brush surface is one with the polymer chains grafted at one end to the surface. The question is how the brush behaves depending on its compatibility with the solvent, expressed by the χ parameter (0 for good, 0.5 for θ, higher for bad). Using Prof Frans Leermakers' implementation of SF theory1, we can readily find out
The polymer has N segments (typically a monomer unit, typically with a unit MWt~80) and is grafted onto the surface with a density φ. If N=100 and MWt=80 then we are talking of a small MWt polymer of 8000, typical of dispersants rather than large polymers. The interactions of the polymer with the solvent are described by the χ parameter. The simulation assumes a number of layers, each one unit thick into which the polymer units might extend. A default assumption is for the number of layers to equal N.
The graph shows the local volume fraction of the polymer chains, φ Polymer, dropping off rapidly at the brush height H. The function φ Solvent is the complement - the volume fraction of solvent molecules.
Prof Leermakers' "simple" algorithm is not as robust as a full SF algorithm, but then we would not be able to run the full algorithm in an app. We give up if the number of iterations exceeds a reasonable limit where it is likely that the algorithm will fail anyway. Success shows the number of iterations, failure shows "No" with a red background.
1SF Theory is a Self-Consistent Field theory of polymers (and other things) in solution and at interfaces developed by Scheutjens and Fleer at Wageningen U in the late 1970s and developed further at Wageningen and other universities.