Cover Picture: Macromol. Theory Simul. 4/2004

Abstract

Cover:The picture on the cover shows the spontaneous curvature in an alternating copolymacromonomer brush with phase separated side chains.Further details can be found in the Full Paper by J. de Jong* and G. ten Brinke on page 318.

One‐ and Two‐Component Bottle‐Brush Polymers: Simulations Compared to Theoretical Predictions

“…As a consequence of our discussion, we call into question the idea of the Janus cylinder‐type phase separation56–58 and propose as an alternative possibility (Figure 31) the “double cylinder” (with cross‐section resembling the number 8). Which of these cross‐sectional structures occur will depend on the interaction parameters $\varepsilon _{{\rm AA}} = \varepsilon _{{\rm BB}}$ , and ε AB , of course.…”

“…In an earlier simulation study of phase separation in binary bottle brushes,57 it was suggested to quantify the degree of separation by considering the distribution of the polar angle φ i from the axis to monomer $\ell$ . Defining a variable $\sigma _\ell ^{\rm A}$ , which is $\sigma _\ell ^{\rm A} = 1$ if monomer $\ell$ is of type A and zero otherwise, and similarly $\sigma _\ell ^{\rm B}$ , de Jong and ten Brinke57 introduced a function and studied P ( ϕ ) varying χ AB . However, it turns out that P ( ϕ ) always has a rather complicated shape, and its dependence on χ AB is rather weak.…”

“…Turning to the problem of intramolecular phase separation in binary (AB) bottle brush polymers, we have examined the proposal that a Janus cylinder‐type phase separation occurs 56–58. This idea is questionable for several reasons: (i) in a quasi‐one‐dimensional system, no sharp phase transition to a state with true long‐range order can occur; at most one can see a smooth increase in the corresponding correlation length, as the temperature is lowered (or the incompatibility between A and B is enhanced, respectively).…”

“…We still consider a bottle brush polymer with a strictly rigid straight backbone, where at regularly distributed grafting sites (grafting density σ ) side chains of length N are attached, but now we assume that there are two chemically different monomeric species, A and B, composing these side chains with N A = N B = N . These systems have found recent attention, suggesting the possibility of intramolecular phase separation 56–58. In a binary system pairwise interaction energies ε AA , ε AB , and ε BB are expected, and consequently phase separation between A and B could be driven by the Flory–Huggins parameter where z c is the coordination number of the lattice, like in the Flory–Huggins lattice model of phase separation in a binary polymer blend 44, 45, 50–52.…”

“…Just as in a binary polymer blend (A,B) typically the energetically unfavorable interaction (described by the Flory–Huggins parameter χ 44, 45, 50–52) should cause phase separation between A‐rich and B‐rich domains. However, just as in block copolymers where A chains and B‐chains are tethered together in a point,53–55 no macroscopic phase separation but only “microphase separation” is possible: for a binary (A,B) bottle brush with a rigid backbone one may expect formation of “Janus cylinder” structures 56–58. This means, phase separation occurs such that the A‐chains assemble in one half of the cylinder, the B chains in the other half, separated from the A‐chains via a flat interface containing the cylinder axis.…”