io-saito / polyfields.jl

A Julia implementation of polymer self-consistent field theory.

PolyFields.jl

PolyFields is a minimal Julia implementation of polymer self-consistent field theory, as described in the extensive monograph "Fredrickson, G. (2005). The Equilibrium Theory of Inhomogeneous Polymers." Core implementation details are heavily inspired by the Fortran package PSCF.

Currently, the package only has the capability of solving the self-consistent field theory (SCFT) equations, corresponding to a mean-field solution of the underlying field-theoretic partition function. Implementation of full field-theoretic simultions (FTS) via complex Langevin sampling is a later goal.

Usage

The PolyFields package is amenable for use in an interactive workspace environment. The basic objects required for a field-theoretic simulation can be created as follows.

using PolyFields

# Number of grid-points in x/y/z dimensions
dims = (64, 1, 1);

# Unit cell for 1D system
cell = UnitCell(1, :lamellar, 10.0); 

# Create monomers, which represent a distinct chemical type
amon = Monomer(; id = 1, vol = 1.0, charge = 0.0);
bmon = Monomer(; id = 2, vol = 1.0, charge = 0.0);

# Create a diblock copolymer species with: N = 100, fA = 0.5, bA = bB = 1.0, Ns = 100
chain = Diblock(amon, bmon, 100, 0.5, 1.0, 1.0, 100);

# Create a Flory-Huggins interaction
itx = FloryInteraction();
set_interaction!(itx, amon, bmon, 0.2);

# Create a system to hold all the pieces
sys = FieldSystem(dims, cell; monomers = [amon, bmon], ensemble = Canonical);
add_species!(sys, chain);
add_interaction!(sys, itx);

# Initialize the fields randomly with a scaling factor of 0.1
fieldinit!(sys; scale = 0.1)

Then, after creating a system and adding the appropriate components, we can run an SCFT calculation. This is done by specifying an AbstractFieldUpdater to relax the field configurations, and optionally the cell configurations as well.

# Runtime options for SCFT
opts = SCFTOptions(nsteps = 1500, nsout = 100, ftol = 1e-4, stol = 1e-4);

# Anderson mixing field updater, with a history size of 10 previous configurations
updater = AndersonUpdater(; nhist = 10);

# Variable cell implementation. Update cell every 5 SCFT steps, and perform 20 iterations
domain = DomainUpdater(; nskip = 5, nper = 20);

# Run the SCFT simulation
scft!(sys, updater; domain = domain, opts = opts)
--------------------------------------------------------------
Step (0     /  1500): ferr = 1.530661e+00, fhelm = 6.70556e-02
Updating cell dimensions: serr = 9.72180e-04
Step (10    /  1500): ferr = 8.668635e-01, fhelm = 7.12575e-02
Updating cell dimensions: serr = 4.82911e-05
Step (20    /  1500): ferr = 3.592973e-01, fhelm = 8.17260e-02
Updating cell dimensions: serr = 2.49362e-05
Step (30    /  1500): ferr = 1.366519e-03, fhelm = 8.12312e-02
Converged @ step = 36: ferr = 6.278932e-06, fhelm = 8.12381e-02
Converged cell parameters: [16.528709413909947]

SCFTResults
  time: Float64 0.0257432
  nsteps: Int64 36
  converged: Bool true
  ferr: Float64 5.0874415525661515e-6
  serr: Float64 1.6582423877606872e-6
  fhelm: Float64 0.0812381288285528

TODO

• Add plotting tools for system and field output
• Ordered initialization: Cell --> System --> Updaters, no setup calls internally
• Add species to system without adding monomers beforehand?
• Divergence issues for AndersonUpdater w/ sub-optimal seeding
• GCE performance and stability, chemical potential constraints
• Add FDDD2 crystal systems, more generic format for basis construction
• Custom field containers -- analogous to NN tensors, stores residuals