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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 = 216σαzj is the position of potential minima, rc = 3.5σ is the potential

cut-off distance and

Uaβ(r) = ⅛



(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



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