Quantized-fold-length polymers such as polyethylene brassylate (PEB) display multiple minima in the crystal growth rate versus crystallization temperature, caused by self-poisoning: unstable stems one repeat unit too short attach to the growth front, linger, and obstruct the growth of stable stems. A 2024 analytical rate-equation model reproduced the two minima of PEB quantitatively, but only piecewise — separate high-temperature (F4–F3) and low-temperature (F3–F2) fits that do not merge — and it left unmodeled the effect of self-poisoning in conventional polydisperse polymers. The open problem is to build a unified, physically validated quantitative theory of self-poisoning at polymer crystal growth fronts: a model treating all relevant stem lengths and their interconversion simultaneously with one consistent parameter set, extended to polymers whose lamellar thickness varies continuously. Follow-up work in 2024–2026 has quantified polymorphic self-poisoning in other systems but has not built this unified treatment.

Background

When a polymer crystallizes from the melt, chains fold back and forth and pack into thin crystalline lamellae; a 'stem' is the straight chain segment between two consecutive folds, and the fold length (lamellar thickness) is the stem length. In classical kinetic theories of polymer crystallization (the Lauritzen–Hoffman framework and its descendants), the crystal growth rate is set by an interplay of secondary nucleation at the growth front and the thermodynamic driving force, with all kinetic complications lumped into a pre-exponential mobility factor. 'Self-poisoning' is a specific kinetic obstruction absent from those theories: stems that are too short to be stable at the given crystallization temperature nevertheless attach temporarily to the growth surface and, because their lifetime is long, block productive growth by stems of stable length. The effect was discovered as anomalous minima and inversions in growth rate versus temperature in ultralong n-alkanes (monodisperse paraffins), where the fold length is quantized — chains crystallize either extended (once-folded, twice-folded, ...) — and at each transition between adjacent quantized thicknesses the growth rate passes through a minimum (Ungar, Stejny, Keller, Bidd and Whiting 1985; Ungar and Keller 1987). Sadler's 'roughness-pinning' theory was an early attempt to fold such surface blocking into growth theory but failed to reproduce most polymer crystal habits. Self-poisoning also appears in simple lattice and simulation models (Ma et al. 2009; Whitelam, Dahal and Schmit 2016) and even in pathologic protein aggregation. Precision polymers revived the phenomenon in macromolecules: in polyethylenes with bromine atoms placed at exactly regular intervals along the chain, a growth-rate minimum appears at the transition between two crystal polymorphs (Zhang et al. 2018). In polyethylene brassylate (PEB), a polyester whose diester 'defects' are spaced by exactly eleven methylene units so that folds lock onto a lattice of integer multiples of the repeat, two growth-rate minima occur at the temperatures where the preferred stem length drops from four repeat units (F4) to three (F3) and from three to two (F2); here F_N denotes the crystal form built from stems N repeat units long (Marxsen et al. 2022). The F_N melting temperatures increase with N, so at lower crystallization temperature the thinner lamella becomes the stable one. Gabana, Gehring, Zeng and Ungar (2024) formulated a one-dimensional steady-state rate-equation model with elementary attachment and detachment of single repeat units plus post-attachment stem lengthening ('stem conversion'), and fitted the crystallization rate curves of three PEB molar masses measured by differential scanning calorimetry (DSC, in the F4–F3 range) and flash scanning calorimetry (FSC, in the F3–F2 range). The fits confirmed quantitatively that the PEB minima are caused by self-poisoning. However, the model is piecewise: the high-temperature and low-temperature fitted branches do not completely merge — plausibly because the low-temperature branch includes F2 attachment and F2-to-F3 conversion that the high-temperature branch omits — and the authors state that a model accounting for all three stem lengths (F4, F3, F2) and their mutual interconversion at the same time is a necessary next step, most likely requiring numerical methods. The 2024 model also deliberately ignores lateral surface energy, primary and secondary nucleation, and the structure of the amorphous–crystal interface. In conventional polydisperse polymers the lamellar thickness changes continuously with undercooling, so discrete minima are not seen; classical theories subsume the self-poisoning retardation inside the pre-exponential viscosity term, and no quantitative treatment isolates it. Beyond fold-length poisoning, adjacent results point to other poisoning mechanisms: crystallization of the stereocomplex from racemic poly(lactic acid) (PLA) is retarded by 'poisoning by purity' — rejection of enantiomeric excess at the growth front (Cui et al. 2023) — and, as the source paper announced and later work confirmed, an unstable but kinetically favored polymorph can poison growth of the stable form, demonstrated for PLA (Yang et al. 2026) and thermoplastic polyurethanes (Baouch et al. 2026). Molecular dynamics simulations of precision brominated polyethylene have begun to expose the microscopic layer-by-layer growth and quantized thickening (Gabana et al. 2024b), and growth-rate minima have now been reported in further long-spaced polyester families (Janani et al. 2025), but neither provides the simultaneous multi-stem-length kinetic model that the 2024 analysis called for.

Problem Statement

Develop a unified quantitative theory of self-poisoning at polymer crystal growth fronts that closes the gaps left by the 2024 piecewise rate-equation model of Gabana et al. for quantized-fold-length polymers, as one coherent objective with two jointly linked requirements. (1) Simultaneous multi-stem-length kinetics: construct a crystal growth model — analytical if possible, otherwise numerical — in which all relevant stem lengths of polyethylene brassylate (F4, F3, F2) coexist on the growth surface with their elementary attachment, detachment, and interconversion (stem conversion) processes treated at the same time, so that the entire experimentally measured crystallization-rate-versus-temperature curve, including both rate minima and the F4-F3/F3-F2 transition region where the previous high-temperature and low-temperature fits failed to merge, is described by a single consistent set of physically meaningful parameters, for each of the PEB molar masses measured by Marxsen et al. (2) Extension beyond quantized systems: give a quantitative treatment of self-poisoning in conventional polydisperse polymers, where lamellar thickness varies continuously with undercooling, isolating the poisoning retardation that classical theories subsume into a pre-exponential factor, and say under what observable conditions it produces detectable anomalies. The problem is solved when a self-poisoning-inclusive description of polymer crystal growth reproduces the full crystallization-rate-versus-temperature data of quantized-fold polymers, including both minima, with a single consistent parameter set, and provides a quantitative treatment isolating the self-poisoning retardation in conventional polydisperse polymers.

References

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