When amphiphilic homopolymers whose pendant groups simultaneously supply hydrogen bonding and aromatic π–π stacking are self-assembled by solvent exchange from tetrahydrofuran into water, they collapse heterogeneously into bowl-shaped nanoparticles (nanobowls) rather than compact spheres: in the founding 2019 system, opening width and interior-hole depth grew approximately linearly with degree of polymerization at nearly constant particle diameter, and removing either interaction — or photo-switching azobenzene to its non-stacking cis form — reverted the product to compact micelles. Later work (2020–2025) generalized bowl formation to other pendant chemistries, a polypeptide backbone, non-THF cosolvents, and even bottlebrush architectures lacking the hydrogen-bond/π–π pair, and supplied qualitative mechanisms (trapped-bubble coalescence, interfacial tension, internal viscosity, exchange kinetics). What still does not exist is the quantitative layer toward which the founding paper's design principle points: measurable parameters and numerical thresholds separating bowl-forming from compact-collapse conditions, and predictive relationships mapping those parameters onto opening width and hole depth. The present problem asks for that quantitative, predictively validated account of morphology selection and geometry control in homopolymer nanobowl self-assembly.

Background

Bowl-shaped polymer nanoparticles — 'nanobowls', particles a few hundred nanometers across with a single concave opening and an interior cavity — are sought as nanoscale containers, concentrators and reactors for catalysis, cargo delivery, sensing and confined chemistry, because the concave geometry and enclosed cavity allow selective uptake and packing of guest species. Early fabrication routes were template-based (laborious and often environmentally unfriendly) or relied on block copolymers, whose sharp boundary between hydrophilic and hydrophobic blocks favors symmetric morphologies such as spheres, cylinders and vesicles; Xu et al. (Soft Matter 2016) exemplify the block-copolymer strategy, generating nano-bowls through three-dimensionally confined assembly and disassembly of polystyrene-b-poly(4-vinyl pyridine).

Sun, Liu and Du (Chemical Science 2019) introduced a fundamentally different, template-free route: self-assembly of a single homopolymer. Amphiphilic homopolymers carry both hydrophilic and hydrophobic moieties on every repeat unit, so they lack a sharp intramolecular phase boundary and can collapse in more diverse ways than block copolymers. They synthesized series of PHAzoMA — poly(2-hydroxy-3-((4-(phenyldiazenyl)phenyl)amino)propyl methacrylate), a methacrylate backbone bearing amino-alcohol groups (interchain hydrogen-bond donors/acceptors) and azobenzene groups (flat aromatic units that stack via π–π interaction) — by RAFT polymerization (reversible addition–fragmentation chain transfer, a controlled radical technique giving narrow molecular-weight distributions) with degrees of polymerization (DP, the number of repeat units per chain) of 10 to 226. Adding water to a tetrahydrofuran (THF) solution of the polymer — a 'solvent switch' that makes water the selective solvent — drove aggregation: DP 10 gave compact particles, while DP 29–226 gave nanobowls whose opening width (242–423 nm) and interior-hole depth (95–363 nm) increased approximately linearly with DP while the overall particle diameter stayed nearly constant (about 530–556 nm by dynamic light scattering). Control polymers with only the hydrogen-bonding pendant (P1) or only the azobenzene pendant (P2) collapsed into compact 'homopolymer complex micelles' (HCMs, dense spherical aggregates), while the polymer carrying both (P3) formed bowls; pre-irradiating azobenzene with ultraviolet light to convert it from the trans to the cis isomer, which cannot π–stack, also abolished bowl formation. The mechanistic picture is heterogeneous collapse: transmission electron microscopy (TEM) snapshots during assembly show preformed spheres developing internal bubble-like voids that coalesce and eventually breach one side. The authors distilled this into a design principle: concurrent hydrogen bonding plus π–π stacking, within an 'appropriate range' of interaction strength and chain mobility, with DP as the geometry knob.

That design principle is explicitly qualitative. The founding paper tested one pendant chemistry, one solvent pair (THF to water) and one fixed protocol, and reported the DP–geometry correlation from single measurements per DP without error bars; the 'appropriate range' of interaction strength and chain mobility was never parameterized. Subsequent work changed this landscape empirically but not quantitatively. Wu et al. (Polymer Chemistry 2022) showed that a second homopolymer, poly(N-([2,2′-bipyridyl]-4-yl)acrylamide) (PBPy, combining amide hydrogen bonding with bipyridine stacking), forms nanobowls with controllable size and denting degree; Jiang et al. (ACS Macro Letters 2025) obtained biodegradable polypeptide-graft nanobowls with dents tunable by initial concentration or by the cosolvents, still via hydrogen-bond/π–π synergy; Huang et al. (Macromolecules 2020) built water-soluble fluorescent nanobowls from rigid conjugated polymers by multiple supramolecular coassembly; and Lin et al. (Chinese Journal of Polymer Science 2021) dented homopolymer nanospheres by co-assembly with a short peptide, relating dent curvature to organic bubbles trapped in protospheres near the critical aggregation concentration (CAC, the concentration at which chains begin to aggregate). Most tellingly, Pal et al. (Macromolecules 2022) found that amphiphilic core–shell cyclic bottlebrush polymers with polystyrene-b-poly(acrylic acid) side chains — which contain no hydrogen-bond/π–π pendant pair at all — also transform spheres into porous spheres and then nanobowls under THF-to-water exchange, with the outcome depending on internal viscosity and the solvent-exchange rate. Bowl formation is thus neither restricted to the founding chemistry nor demonstrably dependent on the synergistic pendant pair; what selects the bowl morphology, and how strongly each variable contributes, remains unquantified. The field's own review of homopolymer self-assembly (Li et al., Chemistry of Materials 2023) still organizes this territory at the level of empirical design principles and qualitative driving forces (hydrophobic effect, electrostatics, hydrogen bonding, π–π stacking, crystallization).

Problem Statement

For the solvent-exchange self-assembly of amphiphilic homopolymers into bowl-shaped nanoparticles, establish a quantitative and predictive account of morphology selection and geometry control. Concretely: (a) identify measurable molecular and process parameters — for example pendant hydrogen-bonding and π-stacking strengths (association constants or binding free energies), chain-mobility measures such as degree of polymerization and glass-transition temperature in the solvent-plasticized state, solvent-composition trajectory and exchange rate, and polymer concentration — that govern whether aggregation ends in compact homogeneous collapse (homopolymer complex micelles) or heterogeneous collapse into a bowl with a single opening and an interior hole; (b) determine the approximate quantitative thresholds in these parameters that separate the morphology regimes, and the functional dependence of opening width and interior-hole depth on the governing parameters, across and beyond the experimentally tested DP window (DP 29–226 in the founding PHAzoMA system); and (c) validate the resulting relationships predictively, without refitting, on at least one homopolymer chemistry or solvent-exchange protocol not used to construct them. A complete answer must be consistent with the pinned observations of the founding and follow-up systems — including the failure of single-interaction pendants (P1, P2) and of the non-stacking cis-azobenzene form to produce bowls, and the formation of bowls by cyclic bottlebrushes that lack the hydrogen-bond/π–π pendant pair — and must therefore delimit when that interaction pair is sufficient and what mobility or kinetic conditions can substitute for it.

References

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