PySFBox — Scheutjens–Fleer SCF lattice theory in pure Python/NumPy

Scheutjens–Fleer lattice SCF in pure Python/NumPy that reads Namics input files and writes Namics output files, so existing input files, analysis and plotting scripts, and course material keep working — no C++ toolchain required.

Install (Python ≥ 3.9; the only dependency is NumPy):

pip install pysfbox            # adds a `pysfbox` command to your PATH
pysfbox my_input.in            # writes my_input.kal / my_input.pro

Or pipx install pysfbox for an isolated, always-on-PATH command-line tool. pysfbox runs from any folder and writes its .kal/.pro next to each input file. Without installing at all — just clone the repo (or drop the pysfbox/ folder next to your inputs) and run the module directly:

pip install numpy
python -m pysfbox my_input.in        # run from the folder that contains pysfbox/

GPL-3.0-or-later (see LICENSE and NOTICE; pysfbox/sfnewton.py carries its own Wageningen copyright notice and governing terms).

Regression tests: python tests/run_tests.py. The tests/ folder doubles as an example collection — every supported feature has a small, commented .in file there (brushes, adsorption, charged walls, weak polyelectrolytes, branched molecules, 2D/3D grids, searches).

Keyword reference: REFERENCE.md documents every input keyword — allowed values, defaults, and what each computes — as a lookup manual.

Validation

PySFBox is validated against the compiled Namics: dozens of regression cases agree with the C++ oracle at or near machine precision, a 28-case exercise set reproduces the compiled Namics output case for case, and thermodynamic observables (free energy, grand potential) agree to the shared convergence floor. A depletion profile additionally cross-validates against an independent SF-SCF implementation to ~4e-13, and the physics has passed two full first-principles reviews with adversarial verification. Where PySFBox departs from Namics it does so deliberately — implementing the corrected physics where Namics has confirmed bugs (the fixed-potential Poisson factor 2, the refined-lattice bond length, the weak-charge free-energy/chemical-potential index terms) — each noted in the relevant section below.

What it supports (v1)

• Input: the Namics key : name : parameter : value format, // comments, start blocks (settings accumulate, like Namics), alias (#N# substitution), and var parameter scans (scan/step/end_value), including alias scans (scan : N-value).
• Lattice: one, two, or three gradient directions (gradients : 1/2/3), as in Namics. 1-gradient: planar, cylindrical, spherical, simple_cubic (λ=1/6) or hexagonal (λ=1/4), lattice refinement FJC_choices : 5, 7, … (spherical/cylindrical), offset_first_layer shifts the radial origin. 2-gradient (simple_cubic, FJC 3, neutral/linear): flat (x,y) and cylindrical (r,z); 3-gradient: flat (x,y,z). N-D uses n_layers_x/y/z and per-axis bounds lowerbound_x, upperbound_y, … (mirror / surface / periodic); one unified finite-volume lattice handles every geometry.
• mon: freedom free / frozen / pinned, frozen_range / pinned_range (1-gradient 1;3, lowerbound, upperbound, firstlayer, lastlayer; 2D/3D box grammar xlo,ylo[,zlo];xhi,yhi[,zhi]), chi_X interaction parameters.
• mol: linear multi-block compositions (X)1(A)200(G)1 AND branched architectures — bracket side chains (C)18[(O)1](O)1... (nestable; several [..][..] on one node), symmetric dendrimers/stars @dend(X,(A)200(G)1,5), combs @comb((B)10;B,(A)25,(B)9,100;(B)1), and group-repeat sugar (C)12((O)1(C)2)5(O)1, on any 1-gradient geometry; freedom free (phibulk), restricted (n or theta), solvent.
• search / super-iteration: var : mol-X : search : theta (or n / phibulk) paired with a target — var : sys-NN : grand_potential : 0, ... : free_energy : V, or var : mol-Y : mu / theta / n / phibulk : V — runs an outer scalar root-find (regula falsi) that adjusts the searched quantity until the target observable hits its value, each step a full warm-started SCF solve. When later start blocks re-trigger the same search (a sweep), each search begins from the previous start's found root rather than the file's declared value. var : sys-NN : Laplace_pressure : 0 (with the delta constraint below) drives the inside/outside pressure difference of a pinned droplet/micelle/membrane to zero; newton : ... : super_deltamax sets the bracket probe factor (1 + super_deltamax; the 0.5 default suits spherical θ~R³ searches — use a small value like 0.01 when θ moves a pinned flat interface).
• Delta constraint (interface pinning): sys : NN : constraint : delta with delta_molecules : A;B, delta_range : (z) (multiple sites (z1);(z2); at FJC_choices > 3 add delta_range_units : bondlength or gritsize) and phi_ratio : r (or critical_ratio = sqrt(N_A/N_B)) pins the local composition at the listed layers: phi_A − phi_B is driven to (r−1)/(r+1) by a Lagrange-multiplier field beta(z) that enters the two molecules' propagators as ±beta. The classic use (cf. the Namics nucleation_barrier.in example): pin the interface and scan phi_ratio (or delta_range) over start blocks to push a micelle/droplet away from its equilibrium size while reading grand_potential — the free-energy landscape F(size) that equilibrium SCF alone cannot reach. The beta work term is included in the free energy and grand potential (F = Ω + Σnμ holds at the solver floor). Profile output pro : sys : NN : beta; oracle-validated on a 52-start micelle-compression scan (tests/delta_micelle.in).
• Electrostatics: mon : valence (fixed charges, strong electrolytes), mon : epsilon (relative permittivity, default 80), mon : e.psi0/kT (fixed surface potential on a frozen electrode layer), mol : freedom : neutralizer (auto-adjusts its bulk fraction for an electroneutral bulk), lat : bondlength (meters). The dimensionless potential psi joins the iteration; profiles via pro : sys : X : psi and q. Works on planar, cylindrical and spherical lattices (the curved Poisson uses face-area-weighted fluxes; tests/charged_sphere.in, tests/charged_cylinder.in match the compiled Namics at the convergence floor, and the spherical potential reproduces analytic Debye–Hückel screening). Validated against the compiled Namics at machine precision (tests/polyelectrolyte_wall.in); fixed-potential systems (tests/edl_fixed_psi.in) validate against Debye theory instead, because PySFBox deliberately corrects a factor-2 bug in the Namics fixed-potential Poisson branch (Debye lengths come out √2 too short there). Refined curved charged lattices (FJC_choices > 3) are supported and refinement-consistent: the Poisson equation keeps the physical bond length, where Namics' Debye lengths scale spuriously with the refinement — so expect a deviation from an unpatched Namics on that combination. Curved fixed-potential electrodes raise a clear message.
• Weak (multistate) charges: state : AH : mon : A + state : AH : valence : 0 attach annealed internal states to a segment; reaction : weak : equation : 1(AH) + 1(H2O) = 1(AM) + 1(H3O) + reaction : weak : pK : 7 set their equilibria; state : H3O : alphabulk : 1e-7 anchors the pH (site-fraction based, as in Namics: "pH" = −log10 alphabulk_H3O). The bulk ionisation is solved to machine precision (Henderson–Hasselbalch exactly, in site fractions with the water activity included); locally every state equilibrates with the fields — charge regulation comes out automatically. Titration scans: var : state-H3O : scan : alphabulk with scale : exponential (steps = steps per decade, as in Namics). Per-state outputs: kal theta_AM, alphabulk_AM, phibulk_AM, theta_exc_AM (on the parent mon), mol : X : mu-AM; pro phi-AM, alpha-AM, u-AM. States inherit the mon's chi (state-level chi overrides); the mon-level valence is ignored once states exist. Validated against the compiled Namics at the convergence floor on the Namics polE.in example and a 73-step titration (tests/weak_*.in); PySFBox implements corrected physics in a few spots where Namics has known bugs, so F/mu comparisons with an unpatched Namics differ whenever state–state chi is nonzero.
• sys: initial_guess — polymer_adsorption / membrane / micelle analytic starting potentials (the Namics formulas, e.g. u = −λ·χ at solid-adjacent sites), honored on the first calculation only, exactly like Namics; previous_result/none accepted; guess files and membrane_torus raise a clear message.
• Solver: the Namics pseudohessian quasi-Newton (a licensed Python translation of sfnewton.cpp) as primary, with Anderson-accelerated Picard and two rescue stages as fallbacks (reads newton : ... : tolerance / iterationlimit / deltamax / m / method; the Namics method choices pseudohessian / DIIS / Picard / LBFGS / hessian map onto this cascade — hessian is the Namics full-Hessian mode, recomputing a finite-difference Hessian every iteration). Propagators are renormalised with log-domain bookkeeping, so long or strongly adsorbing chains cannot overflow. Large 2D/3D grids (beyond the dense pseudohessian) are handled by the Anderson stage.
• Output: .kal (header + one row per calculation/var step, %.16e) and .pro (x at half-integer layers + %.20g columns), with Namics file numbering. Unknown output properties print NiN plus a warning — exactly like Namics. Implemented kal properties: sys grand_potential, free_energy (and free_energy (po)), iterations, residual; lat n_layers / volume; mol theta, theta_exc, phibulk, Mu/mu (chemical potential), mu-STATE, n, N, chainlength, GN, phiM, phiMax, phiMin, <alias>-value; mon theta, theta_exc, phibulk, chi_X, 1st_M_phi_z, 2nd_M_phi_z, RMS, fluctuations, and per-state alphabulk_S / valence_S / phibulk_S / theta_S / theta_exc_S. Profiles (pro): mol : X : phi, mon : X : phi, mon : X : u, mon : X : phi-S / alpha-S / u-S, sys : X : alpha / psi / q.

Beyond this release

Full-Namics features that this release does not implement raise a clear NotImplementedError naming the feature, rather than silently producing wrong numbers — so an input either runs correctly or tells you exactly what it needs. Currently outside scope: ring and asymmetric-dendrimer architectures, initial-guess files, and mesodyn/cleng/teng calculations.

The one-gradient path (planar / cylindrical / spherical, including FJC_choices refinement) covers the full feature set above. The two- and three-gradient lattices — 2D flat, 2D cylindrical (r,z), 3D flat, as in Namics — currently cover neutral linear chains on simple_cubic; charged and branched systems there need gradients : 1. Curved fixed-potential electrodes raise. For weak charges, unbalanced reactions and states on frozen monomers are rejected (the latter also in Namics).

Extending (where things live)

The module layout mirrors the Namics classes, so the C++ original is the roadmap for extensions:

Examples: new output properties = extend the tables in System.get_value / System.get_profile; new chain architectures = generalise the tree walk in Molecule (see mol_branched.cpp).

Convergence envelope

The primary solver IS the Namics quasi-Newton (pseudohessian): sfnewton.py is a faithful, licensed Python translation of sfnewton.cpp, run from the warm-start guess with Namics-like iteration counts. Anderson-accelerated Picard (with a damped-Picard warmup on cold starts) is the fallback, plus two rescue stages (extended-budget pseudohessian, one-shot full-Hessian anchor) for the stiffest cases. This converges the entire shipped validation set, including the extreme corner — very strong adsorption of very long chains (the shipped homopolymer_adsorption.in, N = 10000, chi_Si = -6) converges via the extended rescue and matches the compiled Namics exactly. Genuine non-convergence still fails gracefully (a clear "no convergence" message with actionable advice, never a wrong number). var scans warm-start each step from the previous solution — ramping a parameter (e.g. a co-solvent) is the intended way into hard regimes.

Speed

The default path is deliberately pure NumPy — one dependency, every equation inspectable — running the same pseudohessian quasi-Newton as Namics, with Namics-like iteration counts. On a 28-case benchmark set the compiled Namics C++ takes ~18 s where PySFBox takes ~2 minutes, and every one of those 28 cases matches the compiled Namics output: typical single problems solve in seconds, the stiffest shipped case (homopolymer_adsorption.in, N = 10000, chi_Si = −6) in a few minutes. For throughput-bound parameter sweeps, the same input files run unchanged on the compiled Namics — compatibility works in both directions.

Caveats for quantitative use

• The primary solver is a translation of Namics' quasi-Newton; iteration counts are Namics-like but not identical (fallback stages differ), and converged solutions agree to the shared convergence floor.
• The grand potential and free energy implement the standard uncharged SF expressions; cross-validated against compiled Namics on a two-brush case (free energy 6e-9, grand potential 5e-8 relative — the shared convergence floor; see tests/two_brushes_quick.in). For research use, spot-check your own geometry the same way. Profiles, theta, theta_exc, and moments follow the Namics definitions exactly (LGrad1::Moment, WeightedSum).
• Default tolerance 1e-7, iterationlimit 1000, deltamax 0.1 (as in Namics).

Citing PySFBox

If you use PySFBox in your research, please cite it — GitHub's "Cite this repository" button uses CITATION.cff, and each release is archived on Zenodo with a DOI: 10.5281/zenodo.21338367 (concept DOI, always resolving to the latest version). Please also cite the underlying sfbox/Namics work by Leermakers and co-workers.

Acknowledgements & lineage

PySFBox is a reimplementation of the Scheutjens–Fleer self-consistent-field lattice theory as realised in sfbox/Namics by F.A.M. Leermakers and the Physical Chemistry group at Wageningen University — the input/output formats, property names, and numerical conventions all follow Namics so that existing material keeps working. pysfbox/sfnewton.py is a Python translation of Namics' sfnewton.cpp and carries the original Wageningen University copyright and reproduction notice in its file header, which governs that file. Many thanks to Frans Leermakers for sfbox and Namics — the theory and the code that PySFBox builds on — and for discussions along the way.

PySFBox itself is licensed under the GNU General Public License v3.0 or later (GPL-3.0-or-later) — see LICENSE and NOTICE.