Three-phase coexistence with sequence partitioning in symmetric random block copolymers.

Area of Science:

• Polymer Science and Engineering
• Materials Science
• Statistical Mechanics

Background:

• Random Q-block copolymers composed of incompatible monomer types A and B exhibit complex phase behavior.
• Previous models identified macroscopic A- and B-rich phases or microstructured lamellar phases based on sequence distribution and incompatibility.

Purpose of the Study:

• To investigate the coexistence of macroscopic and microstructured phases in random Q-block copolymers.
• To explore the influence of sequence distribution (Markovian vs. non-Markovian) and incompatibility on phase formation.
• To identify novel phase regions and their characteristics.

Main Methods:

• Development of a microscopic model for random Q-block copolymers with varying block lengths (M) and sequence correlations (λ).
• Analytical derivation of multiphase free energy, explicitly accounting for sequence fractionation.
• Comparison with numerical self-consistent field theory (SCFT) for validation, especially in the continuous-chain limit.

Main Results:

• Identification of four distinct regions in the λ-χ phase diagram, including a novel region where three phases (macroscopic, lamellar, and fractionation-influenced) coexist.
• Demonstration of fractionation (non-Markovian sequence distributions) in the coexistence region, involving sequence exchange between phases.
• Characterization of phase transitions and a multicritical point where A-B segregation vanishes, with critical exponents depending on M for triblock copolymers (Q=3).

Conclusions:

• The study reveals a richer phase diagram for random block copolymers than previously understood, including a unique three-phase coexistence region.
• Analytical free energy calculations accurately capture fractionation and phase behavior, particularly near the multicritical point.
• The findings highlight the critical role of sequence distribution and block length in determining copolymer self-assembly and phase behavior.