6. Polymer chains with degree of polymerization of N are grafted to a flat surface with a density of o/a> chains per unit area, where a is the monomer size. If the ensuing polymer brush has thickness h, the volume per chain is ha?/o. The free energy can be written as the sum of three terms: F ON2 N2 h2 + b 2xb Na2 2ha2 2ha2 KBT where b is monomer volume. (a) What is the physical origin of each term? (b) Derive an expression for the brush height h as a function of N