Identifiability of Molecular Orientation Mechanisms in Electrospun Polymer Fibers — code and results

Code, computed values and figures for the paper

Biber, E. Identifiability of Molecular Orientation Mechanisms in Electrospun Polymer Fibers. Submitted to Macromolecules (2026).

Every number quoted in the paper and its Supporting Information is computed by the scripts here and written to results/*.csv; every figure is drawn from those files or from the same model functions. The paper is a theory paper: no experimental data are generated here. The published records it reanalyses (polystyrene, poly(ethylene terephthalate), poly(2,6-dimethyl-1,4-phenylene oxide), poly(ethylene oxide) and polyoxymethylene) are cited in the paper, and only the values taken from them enter the scripts.

Reproducing the results

Tested with Python 3.13, numpy 2.x (the scripts use np.trapezoid, which needs numpy ≥ 2.0), scipy 1.18 and matplotlib 3.11.

pip install -r requirements.txt
python scripts/run_results.py      # writes all 32 files in results/  (about 5–6 min on one core)
python scripts/paper_figures.py    # draws Figures 1–9 into figures/  (about 15 s)
python scripts/toc_graphic.py      # draws the Table of Contents graphic

Run the scripts from the repository root, and run run_results.py first: Figure 8 reads results/flat_diameter_consistent.csv. run_results.py also accepts one or more result-group names to recompute only those groups (flat, composition, a3, lemma1, a5, bayes, kernel, prop3, forms, coupling, pet), for example python scripts/run_results.py pet; an unknown name stops with the list of valid groups. A fresh run reproduces every file in results/ byte for byte.

Contents

scripts/
    theta_r_span.py      model functions: free-volume diffusivity, flat diameter, drying solutions (Lemma 1), A3 windows
    separability.py      model functions: fading-memory kernels, Bayes factors, functional forms, accumulation maps
    coupling.py          model functions: Route 3 coupling and the measured jet stretch
    run_results.py       computes every quoted value and writes results/*.csv
    paper_figures.py     draws Figures 1–9
    toc_graphic.py       draws the Table of Contents graphic
results/                 32 CSV files, listed below with the sections that quote them
figures/                 Figures 1–9 and the TOC graphic, as PDF (vector) and PNG (600 dpi)

Where each result is used

Section numbers refer to the main text; S-numbers to the Supporting Information.

File	Quantity	Sections
arrest_order.csv	arrest order for non-uniform initial composition	3.2
lemma1_drying.csv	numerical check of Lemma 1 (time-varying evaporation, thinning jet)	S3.1
flat_diameter.csv	flat diameter, Equation (7), against arrest composition and flight time	3.3; S1 (Tables S1–S2)
diffusivity_sensitivity.csv	flat diameter under variation of the transferred diffusivity	3.3 (Table 3); S1
flat_diameter_joint_worst.csv	flat diameter with all inputs varied jointly	3.3 (Table 3); 7.1.2
flat_diameter_consistent.csv	flat diameter from the consistent drying calculation, mode-dependent arrest	3.3; 6.1.1; Figure 8
arrest_composition.csv	arrest composition of polystyrene–chloroform from sorption data	S3.6
a3_inertness.csv	upper diameter for post-arrest inertness (A3)	3.4; 7.1.2; S3.7
a3_sensitivity.csv	sensitivity of the A3 bound to its inputs	3.4
a5_injectivity.csv	injectivity of the accumulation map (A5, Lemma 2)	3.5
a5_splitting.csv	loss of injectivity when jets split	3.5; S3.11
bayes_factors_commitment_error.csv	Bayes factor against error in the committed skin level	4.3; Figure 3b
bayes_factors_prior_width.csv	Bayes factor against prior width	4.3; S3.10
bayes_factors_noise.csv	Bayes factor against noise and number of points	S3.10
kernel_skin_match.csv	fading-memory profiles matched to skin profiles	4.4; Figure 3a
kernel_spectra.csv	the same match for multimode and stretched-exponential kernels	4.4
kernel_timing.csv	position of the maximum against stretching and arrest timing	S3.2 (Table S3)
proposition3_kernels.csv	Proposition 3 checked for five kernels	4.4; Figure 4
proposition3b_bound.csv, proposition3b_clock.csv, proposition3b_scaling.csv	Proposition 3(b) and 4 with a composition-dependent clock	4.4
functional_forms.csv	shell fraction against best-fitting exponential	4.6; Figure 5
functional_forms_crossings.csv	crossing diameters of the two forms	4.6; Figure 5a
functional_forms_separation.csv	separation under monotone maps of increasing steepness	4.6; Figure 5c
functional_forms_free_delta.csv	the same fit with free shell thickness	S3.3
sample_sizes.csv	fibers needed for a second structural channel	5.1
coupling_beta.csv	Route 3 coupling, Equations (11)–(12)	5.2; Figure 6
coupling_check.csv	Equations (11)–(12) checked by direct integration	5.2; S3.9
coupling_jet.csv	jet stretch L from the measured polyamic-acid jet, Equation (8)	5.2; S3.9
route3_sample_sizes.csv	fibers needed for Route 3	5.2
case_study_consistent.csv	polystyrene validity windows and test thresholds	6.1.1; 6.1.4; S3.13; Figure 8
pet_plate_skin_bound.csv	bound on a flight-set skin from the poly(ethylene terephthalate) plate control	6.2.1; S3.17; Figure 9

Licence

Code (scripts/): MIT licence, see LICENSE. Computed values (results/) and figures (figures/): Creative Commons Attribution 4.0 International (CC BY 4.0), see LICENSE-DATA.

Citation

If you use this code or these results, please cite the paper and the archived version of this repository (see CITATION.cff).