Efficient Dynamic Self-Consistent Field Theory with Modified Model B Dynamics

Dynamic self-consistent field theory (D-SCFT) is a powerful method for modeling polymer dynamics. Many implementations employ Model A dynamics, which does not enforce local material conservation. Local conservation, however, is crucial in many processes, for example Ostwald ripening. Model B dynamics conserves material locally but introduces challenges due to its time evolution, which depends on the Laplacian of the chemical potential. This results in a $k^2$ dependence in Fourier space and therefore amplifies short length-scale fluctuations, making numerical instabilities more likely to occur. To address this, we implement a crossover approach: using Model A on short length scales where rapid fluctuations dominate, and Model B on longer scales where local conservation is essential. This is achieved through an Onsager coefficient derived from Rouse dynamics (Kawasaki and Sekimoto, Physica A, 1988) within the framework of external potential dynamics (Maurits and Fraaije, J. Chem. Phys., 1997). This method enables stable and efficient D-SCFT simulations while maintaining the necessary local conservation over relevant length scales.