PSCF+: An Extended and Improved Open-Source Software Package for Polymer Self-Consistent Field Calculations

We introduce PSCF+, an extended and improved open-source software package for polymer self-consistent field (SCF) calculations of block copolymer self-assembly. PSCF+ supports various chain models (including the continuous Gaussian chains, discrete Gaussian chains, and freely jointed chains), nonbonded isotropic pair repulsions (including the Dirac δ-function, Gaussian, soft-sphere, and dissipative particle dynamics potentials), and system compressibility (compressible vs incompressible), thus enabling direct comparisons with molecular simulations and field-theoretic simulations based on the same model system without any parameter-fitting. Several recently proposed algorithms are implemented in PSCF+ to greatly reduce the GPU memory usage and speed-up the SCF calculations, including the Richardson-extrapolated pseudospectral methods for solving the modified diffusion equations, the crystallographic discrete cosine transforms taking advantage of the partial symmetry of some ordered phases, and the "slice" algorithm for storing chain propagators. It also avoids redundant calculations and storage of propagators for chain architectures such as bottlebrush block copolymers, and uses an improved iterative scheme for solving SCF equations in athermal solvent conditions. Last but not least, it implements the automated calculation along a path to efficiently calculate free-energy curves and phase boundaries. PSCF+ is freely available and remains under active development, with further extensions planned to broaden its applicability to more complex polymeric systems.