where n(z) is the density, Φ[n(z)] is the grand potential functional, h is the brush height, z is the distance from the surface and µ is the Lagrange multiplier. The grand potential functional composed of three terms. The first term is called the entropic elasticity term and it measures the amount of elasticity that is produced by entropy of the monomers. The second term is called the excluded volume interactions term and it says that no two monomers can not occupy the same place. The third term says that the total number of monomers in the system is fixed. Now that we have the most probable grand potential functional, we can calculate the Physical properties of the system out of that. Here are three coupled equations which do the job.