Numerical Simulation Of Phase Behaviors Of Symmetrical Triblock Copolymers On Sphere

The self-consistent field theory(SCFT)is one of the most successful theories to describe the steady-state phase behavior of block copolymers.Numerical experiments show that it is in good agreement with the experimental results.This paper mainly uses the self-consistent field theory to study the ABA coil-rod-coil triblock copolymers for the phase behavior on the sphere,the coil chain uses the propagator equation derived from the Gaussian chain model,and the rod chain uses the propagation equation derived from the worm-like chain model.The solution of the propagation equation is mainly calculated by splitting the operator for each operator.Local minimum of the Hamiltonian energy is obtained by iterative self consistent field equation,The density distribution and direciton of the Hamiltonian local minimum are the spatial density distribution and direction of the phase structures.The model involves several parameters,such as the isotropic Flory-Huggins interaction ?N,the anisotropic Maier-Saupe orientation interaction ?N,the volume fraction of the coil chain f,the length-diameter ratio of the rigid molecule ?,the persistence length of the rod chain ? and the radius of the sphere R.In this paper,we obtain the changes on the phase structure with the proportion of the coil chain component(f = 0.50,f = 0.66),radius of the sphere R.Through numerical experiments,we obtain spot phase,helical phase,lamellar phase,pore-like phase,dumbbell phase.When f = 0.5,the differences between the steady-state lamellar phases of AB rod-coil copolymers and ABA triblock copolymers at the same radius R were studied,and the Hamiltonian changes of the lamellar phase structure with the change of R were ploted.In the spot phase,the spatial density distribution and index number of singularities of direction are studied,the phase transition relationship between the spot phase and the sphere radius R is given.At f = 0.66,the topological structure types of the spiral phase were studied by rotation and compared with the spatial density distribution of the spiral phase obtained by numerical simulation.The theoretical spiral phase structures were all presented in the numerical simulation;In addition,the dumbbell phase and pore-like phase structure,we plot the spatial density distribution.Finally,we use the asymptotic method to study transition boundary of ISO-Nematic and Nematic-Smectic-A(? = ?)in two-dimensional plane.Compared theoretical phase transition boundary with the numerical simulation results,theoretical results are in good agreement with numerical results.