Mesoscale simulation of polymer reaction equilibrium: Combining dissipative particle dynamics with reaction ensemble Monte Carlo. II. Supramolecular diblock copolymers.

We present an alternative formulation of the reaction ensemble dissipative particle dynamics (RxDPD) method [M. Lisal, J. K. Brennan, and W. R. Smith, J. Chem. Phys. 125, 16490 (2006)], a mesoscale simulation technique for studying polymer systems in reaction equilibrium. The RxDPD method combines elements of dissipative particle dynamics (DPD) and reaction ensemble Monte Carlo (RxMC), and is primarily targeted for the prediction of the system composition, thermodynamic properties, and phase behavior of reaction equilibrium polymer systems. The alternative formulation of the RxDPD method is demonstrated by considering a supramolecular diblock copolymer (SDC) melt in which two homopolymers, A(n) and B(m), can reversibly bond at terminal binding sites to form a diblock copolymer, A(n)B(m). We consider the effect of the terminal binding sites and the chemical incompatibility between A- and B-segments on the phase behavior. Both effects are found to strongly influence the resulting phase behavior. Due to the reversible nature of the binding, the SDC melt can be treated as the reaction equilibrium system A(n)+B(m)right harpoon over left harpoonA(n)B(m). To simulate the A(n)+B(m)right harpoon over left harpoonA(n)B(m) melt, the system contains, in addition to full A(n), B(m), and A(n)B(m) polymers, two fractional polymers: one fractional polymer either fA(n) or fB(m), and one fractional polymer fA(n)B(m), which have fractional particles at the ends of the polymer chains. These fractional particles are coupled to the system via a coupling parameter. The time evolution of the system is governed by the DPD equations of motion, accompanied by random changes in the coupling parameter. Random changes in the coupling parameter mimic forward and reverse reaction steps as in the RxMC approach, and they are accepted with a probability derived from the expanded ensemble grand canonical partition function. Unlike the original RxDPD method that considers coupling of entire fractional polymers to the system, the expanded ensemble framework allows a stepwise coupling, thus greatly increasing the efficiency of the RxDPD approach. The RxDPD technique rigorously satisfies thermodynamic equilibrium, but not the hydrodynamic behavior. However, the approximate treatment of the hydrodynamics can be minimized by simulating a large number of particles.