Multiple polylogarithms are equipped with rich algebraic struc-tures, including the motivic coaction and the single-valued mapwhich both found fruitful applications in high-energy physics. Inrecent workarXiv:2312.00697, the current authors presented a con-jectural reformulation of the motivic coaction and the single-valuedmap via zeta generators, certain operations on non-commutingvariables in suitable generating series of multiple polylogarithms.In this work, the conjectures of the reference will be proven formultiple polylogarithms that depend on any number of variableson the Riemann sphere.
Branched poly(vinyl alcohol) (PVA) was synthesized via chemical modification of linear PVA with epichlorohydrin in an alkaline aqueous medium under conditions preventing crosslinking. Branching was confirmed by IR and Heteronuclear Single Quantum Coherence (HSQC) spectroscopy, as well as by viscometric analysis. An iterative procedure is proposed for refining the branching factor (g) and the viscosity-average molecular weight of the branched macromolecules. Coil diameters determined by viscometry and dynamic light scattering showed satisfactory agreement. While an increase in the viscosity-average molecular weight of branched PVA enhances its surface activity in the low-adsorption region, the branched geometry itself hinders subsequent adsorption due to steric shielding of the interface. This correlates with wetting behavior on Teflon: lightly branched PVA requires a higher concentration to induce wetting inversion than its linear counterpart but further increase in molecular weight shifts the inversion point to lower concentrations due to a higher density of hydroxyl groups. Concurrently, the concentration dependence of the work of adhesion degenerates with increasing molecular weight. Despite their reduced adsorption capacity, the specific geometry of branched PVA macromolecules provides effective steric stabilization of micrometer-sized particles during styrene suspension polymerization. These results demonstrate that chain branching in PVA is a powerful tool for tuning its adsorption properties, stabilizing ability, and interfacial activity.
Cannabinol (CBN) is a highly lipophilic phytocannabinoid whose biomedical application is limited by poor water solubility. In this study, colloidal hydroxyapatite nanoparticles (nHAp) were evaluated as a carrier for CBN, and their effect on model lipid membranes was investigated. Interactions between CBN and lipids were examined using Langmuir monolayers and lipid bilayers (black lipid membranes, BLMs). Langmuir monolayer studies revealed strong interactions between CBN and lipids, resulting in changes in isotherms, compressibility, and monolayer stability. BLM measurements indicated that delivery of CBN via nHAp modifies the electrical properties and stability of the lipid bilayer, suggesting alterations in membrane organization and permeability. These results demonstrate that hydroxyapatite nanoparticles can effectively serve as a carrier for cannabinol while modulating its interactions with lipid membranes.
Imidazole-based ionic liquids hold immense potential in the field of mineral flotation due to their tunable properties. In this study, three imidazole-based ionic liquids with varying carbon chain lengths (OMB, DMB, and HMB) were selected as collectors for quartz flotation to systematically investigate the microscopic mechanisms by which carbon chain length influences the agglomeration and flotation behavior of quartz. Flotation tests and online particle-bubble monitoring (PBM) results indicate that the elongation of the collector's carbon chain significantly enhances its collecting ability and reduces the required reagent dosage. To achieve the complete recovery of quartz in a neutral system, a dosage of 35 mg/L is required for OMB, whereas HMB requires only 8 mg/L. As the carbon chain lengthens, the optimal pH range for highly efficient flotation shifts from alkaline to neutral-acidic. Interfacial measurements and mechanistic analyses (Zeta potential and FTIR spectroscopy) confirm that the imidazole ring of the collector physically adsorbs onto the quartz surface through the synergistic action of electrostatic forces and hydrogen bonding, thereby inducing the hydrophobic agglomeration of particles. Notably, in a strongly alkaline system (pH = 11), the long-chain HMB promotes the formation of oversized quartz agglomerates. This leads to a depletion of free reagents in the liquid phase and destabilizes the bubble liquid film, ultimately triggering a sharp decline in recovery. Density functional theory (DFT) calculations further corroborate the structure-activity relationship at the molecular level: the extension of the carbon chain increases the highest occupied molecular orbital (HOMO) energy and electron-donating ability. The adsorption energy of HMB on the quartz (001) surface reached -350.2 kJ/mol, exhibiting the strongest solid-liquid interfacial affinity. This study elucidates the competitive mechanism of carbon chain length in regulating electrostatic adsorption, hydrophobic agglomeration, and froth stability, providing a solid theoretical foundation for the molecular design of novel green flotation reagents for quartz.
