Microphase Segregation of Diblock Copolymers Studied by the Self-Consistent Field Theory of Scheutjens and Fleer.

Merve Mocan,Frans Leermakers,Marleen Kamperman

doi:10.3390/polym10010078

Abstract

We used the self-consistent field (SCF) formalism of Scheutjens and Fleer (SF-SCF) to complement existing theoretical investigations on the phase behavior of block copolymer melts. This method employs the freely jointed chain (FJC) model for finite chain length and systematic differences exist compared to the classical SCF predictions. We focus on the critical and hexagonal (HEX) to lamellar (LAM) phase transition region at intermediate and strong segregations. Chain length (N) dependence of the critical point () was found to be . The characteristic spacing (D) of LAM was found as at the critical conditions. We present SF-SCF predictions for the phases single gyroid (SG), double gyroid (DG) and hexagonally perforated lamellar (HPL), in the region where HEX and LAM compete. At , ; we found SG and HPL were metastable with respect to LAM or HEX, DG was stable in a narrow region of the asymmetry ratio. In contrast to the latest predictions, at strong segregation , DG was found to be metastable. From the structural evolution of HPL, we speculate that this may be an intermediate phase that allows the system to go through various connectivity regimes between minority and majority blocks.

Highlights

IntroductionThe phase diagram is characterized by a critical volume fraction and a critical interaction parameter
When two chemically different polymers with a small but positive interaction parameter χ are mixed, when time permitted, they will demix into two macroscopic phases of which one is rich in one polymer and depleted in the other while the other phase obtains the opposite composition [1].The phase diagram is characterized by a critical volume fraction and a critical interaction parameter.When the two polymers are long the critical volume fraction is, for symmetry reasons, φcr = 0.5, while the critical interaction parameter decreases with the chain length (N) as χcr = 2/N
We believe that the SF-self-consistent field (SCF) method is appropriate to investigate microphase segregation of block copolymers and remains accurate at strong segregation because of the non-local contributions in the segment potentials being considered

Summary

Introduction

The phase diagram is characterized by a critical volume fraction and a critical interaction parameter. When the two polymers are long (each composed of N segments) the critical volume fraction (φcr ) is, for symmetry reasons, φcr = 0.5, while the critical interaction parameter (χcr ) decreases with the chain length (N) as χcr = 2/N. One finds power-law behavior of the interfacial tension (γ) γ ∝ (∆χ)α = (χ − χcr )α , the density difference between the phases (∆φ) ∆φ ∝ (∆χ) β and width of the interface W = (∆χ)δ. The first two tend to go to zero (both α and β are larger than zero), whereas the latter quantity diverges (δ < 0), upon an approach towards the critical point.

Results

Discussion

Conclusion