Abstract Recently, Frank–Kasper spherical phases have attracted increasing interest in the field of block copolymers and even soft matter due to their complex packing motifs, nonuniform spherical-domain sizes, and unique thermodynamic stabilization mechanisms. Previous self-consistent field theory (SCFT) studies have shown that the stability of Frank–Kasper phases is closely related to the spontaneous curvature of block copolymers, which arises from a competition between the chain stretching of the A blocks versus the chain stretching of the B blocks. Increasing the spontaneous curvature through molecular design can broaden the stability window of spherical phases and allows spherical domains in different coordination environments to adjust their sizes to relieve packing frustration, thereby packing into the complex σ and A15 crystal lattices. However, Frank–Kasper phases were often experimentally observed in low-molecular-weight and weakly entangled block copolymers, where thermal fluctuations may play an important role. Since such fluctuations cannot be included into SCFT, their influence on the formation of Frank–Kasper phases remains unclear. Here, we employ Langevin field-theoretic simulations (L-FTS) to investigate the self-assembly of ABn (n = 2, 3, 4) miktoarm star block copolymers, focusing on how thermal fluctuations affect the stability of Frank–Kasper phases. Our results show that, at a large invariant polymerization index, such as N̅ = 105, thermal fluctuations substantially shift the order–disorder transition boundaries near the weak segregation regime but do not alter the relative stability among the σ, A15, and cylindrical phases significantly. Away from the ODT boundary, thermal fluctuations do not change the characteristics of size differences between those nonequivalent spherical domains in the Frank–Kasper phases. However, near the ODT boundary, widened interfaces together with increased thermal fluctuations may weaken the instantaneous size contrast between different domains. Overall, our results indicate that, when N̅ is large or the system is far from the ODT boundary, thermal fluctuations have a limited effect on the stability of complex Frank–Kasper spherical phases, and the SCFT predictions are reliable.
Abstract We study the mechanical response of a single polymer globule in a poor solvent subjected to oscillatory stretching forces using scaling theory and coarse-grained molecular dynamics simulations. Under constant loading, increasing the applied force induces a first-order globule-stretching transition accompanied by the formation of tadpole conformations at a temperature-dependent characteristic force. Under periodic loading, the delayed response of the polymer gives rise to extension hysteresis, and the associated energy dissipation is quantified by the hysteresis area. Below the unfolding threshold, the dissipative response is controlled by the intrinsic relaxation of the compact globule, and the data collapse onto a universal master curve when the driving frequency is rescaled by the equilibrium relaxation time. At and above the unfolding threshold, a force-induced dynamic phase transition between compact and stretched states gives rise to an additional low-frequency dissipation peak associated with repeated unfolding and refolding of the globule. The crossover between the driven phase transition and the relaxation of the globular state is remarkably sharp near the force-induced globule-stretching transition, where small changes in the driving frequency can increase the dissipated energy by an order of magnitude. These results establish a physical framework for understanding the mechanics of polymer globules subjected to time-dependent forces.
Abstract The properties of polyelectrolytes depend on the counterions that neutralize their backbone. Although the effects of counterion valence and size have been studied, the influence of charge topology, i.e., the spatial distribution of charge within a multivalent counterion, has not been investigated experimentally. We address this question by comparing aqueous solutions of carboxymethyl cellulose (CMC) containing conventional divalent metal ions with solutions containing the organic ditopic counterions hexamethonium and suxamethonium. Conductivity measurements indicate comparable counterion dissociation at low polymer concentrations but substantially greater dissociation of the ditopic ions at higher concentrations. SAXS measurements reveal corresponding structural differences: CMC with ditopic counterions exhibits correlation peaks and smaller stretching parameters, consistent with a larger effective polymer charge and reduced local chain folding, whereas CMC with monotopic divalent metal counterions displays broad correlation shoulders, consistent with weaker electrostatic correlations. Partially “dangling” condensed ditopic ions provide a possible explanation for the observation that the monotopic and ditopic counterions show similar fractions of free counterions from conductivity at low concentrations, while the SAXS profiles indicate a higher effective charge for the ditopic salts. However, this mechanism cannot be established unambiguously from the present conductivity and scattering measurements. Overall, the results demonstrate that counterion charge topology provides a tuneable parameter for controlling polyelectrolyte conformation and charge transport.
Abstract Nile Red fluorescence reveals three distinct phase-separation pathways in heterotelechelic HS–PNIPAM–COOH: multistage, monotonic, and suppressed transitions. Aqueous HS–PNIPAM–COOH (Mn ≈ 6 kDa) is investigated over pH 3–10 and at NaCl concentrations from 0 to 1.0 M using fluorescence, turbidimetry, dynamic light scattering, and temperature-controlled single-particle tracking. Multistage transitions, comprising an initial fluorescence rise, an intermediate plateau, and a second rise, occur under weakly ionised, high-salt conditions. Intermediate conditions produce a monotonic fluorescence increase, whereas strongly ionised, weakly screened conditions suppress detectable phase separation. The multistage sample, citrate buffer containing 1.0 M NaCl, forms stable, micrometre-scale PNIPAM-rich droplets with no further growth across the fluorescence plateau despite increasing turbidity. Growth resumes only above the plateau. By contrast, the representative monotonic samples (citrate buffer without added NaCl and borate buffer containing 1.0 M NaCl) show continuous droplet growth during the temperature holds. On cooling from 60 to 40 °C, multistage droplets remain nearly unchanged in size before undergoing delayed, rapid, collective dissolution at lower temperature, whereas monotonic droplets shrink progressively before later rapid dissolution. These results show that pH and NaCl concentration control both the phase-separation pathway and mesoglobule persistence, producing different high-temperature states that rehydrate differently on cooling.
Abstract CO2-derived aliphatic polycarbonates have attracted considerable attention as sustainable polymeric materials; however, their relatively low glass transition temperature and limited thermal stability restrict their applications in high-performance engineering materials. Herein, a series of benzoxazine-functionalized CO2-derived block copolymers, poly(cyclohexene carbonate)-b-poly(styrene-alt-1-(3-phenyl-3,4-dihydro-2H-benzoxazin-6-yl)-1H-pyrrole-2,5-dione) (PCHC-b-PSHPMIBZ), were successfully synthesized through sequential ring-opening copolymerization (ROCOP) of cyclohexene oxide and CO2 and reversible addition–fragmentation chain-transfer (RAFT) polymerization. The thermal properties of the resulting block copolymers were systematically tailored by varying the PSHPMIBZ contents followed by thermal ring-opening polymerization (ROP). During thermal curing, the benzoxazine units simultaneously generated a covalently crosslinked network and abundant phenolic hydroxyl groups, which established extensive intermolecular and intramolecular hydrogen-bonding interactions with neighboring carbonate and imide carbonyl groups. The thermal ROP mechanism and structural evolution were comprehensively elucidated using differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), in situ Fourier-transform infrared (FTIR) spectroscopy, two-dimensional (2D) correlation FTIR spectroscopy, and solid-state 13C NMR spectroscopy. These complementary analyses revealed that hydrogen-bonding formation occurred immediately following benzoxazine ring opening, producing a hierarchical dual-network architecture composed of covalent crosslinks and supramolecular hydrogen bonds. Consequently, the glass transition temperature of PCHC-b-PSHPMIBZ51 increased dramatically from 115 to 199 °C, while the char yield increased from 0.9 wt % for the corresponding PCHC-b-PSHPMI51 copolymer to 25.3 wt %, and further to 38.3 wt % after post-curing at 270 °C. The cured block copolymers retained homogeneous morphology despite extensive crosslinking, demonstrating that benzoxazine functionalization provides an effective molecular design strategy for converting sustainable CO2-derived polycarbonate block copolymers into thermosetting materials with substantially elevated glass transition temperatures and enhanced thermal resistance.
