Scaling Theory of Planar Brushes Formed by Branched Polymers

Abstract

The equilibrium structure of planar brushes formed by flexible, regularly branched (comblike and starlike macromolecules), and randomly branched polymers is considered. The diagrams of states in τ,σ coordinates (τ = (T - Θ)/T is reduced temperature and σ is grafting area per chain) are constructed, and power-law dependencies for the brush thickness H are obtained. It is shown that due to the existence of two different length scales characterizing comblike macromolecules, the scaling behavior of a combed brush is more varied than that of conventional brushes formed by linear chains. Weakly overlapping combs exhibit behavior similar to that of a conventional brush in a good solvent (H ∼ σ -1/3 ) even at the Θ-point. Strongly overlapping combs rearrange their local structure and recover the exponents for linear brushes in a good solvent (H ∼ σ -1/3 ) and Θ-solvent (H ∼ σ -1/2 ). For marginal solvents, intermediate between good and Θ-solvents, combed brushes exhibit a new exponent (H ∼ σ -5/13 ). Brushes formed by starlike and randomly branched polymers demonstrate conventional σ-dependencies similar to linear chains. However, the molecular-weight dependencies of the brush thickness H for randomly branched polymers are different.