5.2 Model system and theory
The symmetric diblock copolymer molecule is modeled as a freely jointed chain
of tangentially bonded spheres (segments) of two types. One type of segment forms
the ‘A’ block and the other type forms the ‘B’ block. Each block has N segments.
Although both type of segments have the same segment size, σ, they have different
long range attractions. These attractions are modeled as a perturbation to the 6-
12 Lennard-Jones (LJ) potential in the spirit of Weeks-Chandler-Anderson (WCA)
perturbation theory [120, 121].
≤(H = *
uaβ(rmin) uaβ(rc)
uaβ(r) - uaβ(rc)
ff ^aβ < f ≤ ʃ'min
ɪf rmin <r <rc
(5.1)
where rmin = 21∕6σαzj is the position of potential minima, rc = 3.5σaβ is the potential
cut-off distance and
Uaβ(r) = ⅛aβ
(5.2)
The energy parameters, = евв = ɛ and eAB — O- Hence in the model, e quantifies
the incompatibility between the two blocks of the diblock copolymer. Traditionally,
this incompatibility has been characterized by the Flory-Huggins interaction parame-
ter, χ. As discussed by Frischknecht et. al. [50], for a symmetric diblock copolymer, χ
can be related to the incompatibility parameter e for the continuous potential model
118