Bending moduli of dendritic polymer brushes in a good solvent

Abstract

The effect of branching on the Helfrich mean k _C and Gaussian k _G bending moduli of polymer brushes consisting of dendrons grafted to both sides of a thin impermeable surface (membrane) is studied theoretically. The case of an athermal solvent is considered. The moduli are calculated from a change in the free energy of a brush upon cylindrical and spherical bending of the grafting surface, respectively. The grafting density σ, the total number of monomer units N, and the number of generations g in tethered dendrons are varied. Two variants of the self-consistent field method are applied: the analytical approach and the numerical Scheutjens-Fleer method. The first method is applied at small values of σ, when the density profile of monomer units of grafted chains is parabolic in shape. The second method is free of these restrictions. The universal ratio between moduli is found: k _G =−64/105k _C . Both methods predict that the values of moduli decrease with increasing g at constant N and σ. The scaling dependence N ³ remains valid for the moduli of dendritic brushes with different generation numbers g at all of the considered values of σ. The analytical approach also gives the universal scaling dependence k _C ∼ k _G ∼ σ^7/3; however, the numerical method predicts that the dependences of moduli on σ become stronger with increasing degree of branching of tethered dendrons.