Self-Consistent Field Simulation Of Semi-Rigid Diblock Copolymers

The semi-rigid diblock copolymer equations studied in this paper are a 4-dimensional problem,which includes a chain length of 1 dimension,pointing to2 dimensions and 1 dimension of space.Based on the average self-consistent field theory of the worm chain model,we use the operator splitting method combined with spherical harmonic expansion,fast fourier transform to discrete semi-rigid two-block copolymer equations.In the solution process,we need to find the saddle point of the equilibrium state.At this time,we choose the steepest descent method to up-date the external field function and find the period.The phase structure is obtained by calculation:including disordered phase、nematic phase、double-layered Smetic-A phase、single layer of Smetic-A phase、single layer of Smetic-C phase.In addition,the paper also studies the relationship between energy and cycle,the influence of parameters on the cycle;the effect of the step size on the convergence rate;the relationship between the force parameterof Flory-Huggins and the monomer distribution of the copolymer;the analysis of the field functions M（z）,₊（z）,_-（z）,Finally,we simply describe the phase diagram.Three layered phase structures are obtained by numerical experiments,the er-ror and energy in the convergence process are drawn.When the influence of the parameters on the period are studied,1),increased,and the period decreased;whileincreased,the period increased;The iterative step size and convergence speed are analyzed,the convergence speed and maximum iteration step size of each phase structure are different,it can be seen from the table that the phase structure of the Smetic-A phase is relatively slow,the maximum iteration step size is relative-ly small;The resulting phase diagram is compared with the phase diagram of the rigid-flexible diblock copolymer and found to be similar.