Elasticity of Comb Copolymer Cylindrical Brushes

Abstract

An analysis of the cylindical brush of an isolated comb copolymer molecule consisting of a semiflexible backbone and flexible side chains is presented. Using the Alexander-de Gennes approximation, we calculate the free energy of both straight and bent cylindrical brush and the brush persistence length λ, and show that λ scales as a function of the side chain length M as λ ∝ M 2. The discrepancy between the asymptotic scaling behavior and recent computer simulation results is also discussed.

Comb Copolymer Brush with Chemically Different Side Chains

“…This result coincides with the one obtained in ref 5 and is very similar to refs 42 and 43 except for the entropic ln 2 term, which is not present in the cited works due to the difference in the system studied. Now let us estimate the thickness of the interface region.…”

“…and E is the analogy of the particle's energy, which will be implicitly calculated further on (for details see ref 5).…”

“…With reasonable accuracy, the solution of eq 10 can be approximated as 5 Here E A and E B follow from the normalization eq 11.…”

Ring comb copolymer brushes

“…6,13 In general, the presence of a large number of side chains results in severe stiffening of the structure leading to cylindrical comb copolymer brushes ͑or molecular bottle-brushes͒. These molecules have also been investigated theoretically [14][15][16][17][18] and with computer simulations [19][20][21][22][23][24][25][26][27][28][29][30] in some detail. Our studies focused mainly on the persistence length as a measure of the stiffness.…”

“…Theoretical arguments supporting this assertion have been put forward. 17,18 In this paper we will address ring comb copolymers and focus on the influence of the side chain length on the conformational characteristics for a given high grafting density, for flexible and rigid side chains. We will use the elements of the radius of gyration tensor of the backbone to characterize its shape.…”