Mean Field Model Of Charged Diblock Copolymer In Solution And Its Simulations

The SCFT (Self-consistent Mean Field Theory) of polymer is a coarse-grainedmodel which is based on the mean feld assumption. It has been widely applied tostudy the equilibrium phase structures and phase diagrams for polymer systems,where the monomer distribution, topologies and other details of the chain moleculesare also taken into account. In this paper, we use SCFT to research the phaseseparation of the charged diblock copolymers in three-dimensional spherical shellwhich is immersed in NaCl salt solution. The one end of all diblock copolymermolecular chains is fxed to the surface of the spherical particles, while the otherend is free to move. From the microscopic Hamiltonian which accounts for theinteraction bewteen monomers, solvent and mobile ions, the partition function inthe canonical ensemble can be expressed as a functional integral from which themean feld equation are derived from based on the saddle point approximation(mean feld assumption). We solve the mean-feld equations by using a simpleiterative scheme where in each iteration the operator splitting scheme and thespherical harmonic expansion are used to calculate the propagation functions andpotential function, respectively. Numerical results in the case of certain parametersshow that all physical quantities depend only on the radius of the spherical shell.