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Using $365$ days per year, the required time is $2\times 365\times 24=17520\mathrm{h}$. Hencelithium transfers one electron per atom, soThis is the stoichiometric minimum for one cell, or one cell-equivalent parallel assembly, with complete utilization and no self-discharge. Practical loading must be larger. If a pack uses several cells in series, each series cell must carry the full delivered charge and the total lithium mass increases accordingly; no required pack voltage or series count is supplied.

For the specified $x=1$, the discharge half-reactions and their sum areEach mole of CF formula units consumes one mole of lithium and transfers one mole of electrons. For general $x$, the corresponding formula-unit reaction would be ${\mathrm{CF}}_x+x\mathrm{Li}⟶\mathrm{C}+x\mathrm{LiF}$.

Use a lithium-metal negative electrode and a carbon-monofluoride composite positive electrode, separated by a porous, electrically insulating battery separator wetted by a lithium-salt electrolyte in a suitable nonaqueous solvent. Conducting carbon and a binder provide electronic contact through the fluorinated-carbon electrode to its electric current collector; the lithium electrode has its own electric current collector. A sealed stacked or wound assembly supplies useful area and contains the electrolyte.

During discharge lithium is the anode and the carbon-monofluoride composite is the cathode. lithium ions move through the electrolyte while electrons flow through the external load. The battery separator prevents electronic shorting while permitting ionic transport. An aqueous electrolyte is unsuitable because metallic lithium reacts with water. The requested very long operating time requires enough active material and low self-discharge, not merely a high nominal voltage.

The rigid naphthalene core fixes the separation and directions of the two arm attachment points. In A they point from more separated regions of the core, so closure requires the flexible arms to span the core and adopt less favorable torsional arrangements. In B the closer, more convergent attachment geometry permits the UPy ends to meet with less conformational strain and better preorganization.

Both rings gain similar local UPy hydrogen-bonding interactions, but A pays a larger deformation cost in its linkers and overall geometry. That can rationalize its higher calculated total energy and its greater tendency to open into intermolecular chains.

The quoted $50\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ is large compared with $RT\simeq 2.48\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$. Nevertheless a total-energy difference is not automatically a solution Gibbs free-energy difference: solvent and entropy contributions would be needed before converting it into an equilibrium population ratio.

Use two-dimensional NOESY, or ROESY where molecular tumbling makes NOESY less favorable, to look for through-space correlations between proton sites on the two ends that are brought together in the closed conformation. Assign resonances first and compare predicted ring contacts with an open reference or model.

The nuclear Overhauser effect involves NMR cross-relaxation through magnetic dipole–dipole coupling. Its strong approximate $r^{-6}$ dependence makes it sensitive to short interproton distances. A NOESY cross-peak therefore reports spatial proximity, including between sites far apart along the covalent skeleton; it is not a NMR scalar coupling transmitted along that skeleton.

Run a dilution series: end-to-end contacts that persist at concentrations where intermolecular association is negligible support intramolecular ring closure. Hydrogen-bonded NH chemical shifts and diffusion measurements can support the assignment, but neither alone proves ring topology. A flexible open chain can transiently bring ends together, and intermolecular contacts can also give NOEs. Several geometry-consistent cross-peaks, concentration behavior and controlled mixing times make the case much stronger than one peak.

DMSO is a strong hydrogen-bond acceptor. It competes for the NH donors of the UPy units and solvates the association sites, weakening their mutual hydrogen bonding.

For A, the intermolecular chains should shorten or dissociate, reducing the association-driven viscosity. For B, the intramolecular ring should become less populated, increasing the fraction of open conformations. Sufficient DMSO also weakens rings of A and any intermolecular associations of B. The covalent molecular skeletons remain intact.

The extent depends on DMSO fraction and the association free energies in the mixed solvent. solvent viscosity itself also changes, so the prediction concerns the supramolecular contribution rather than an unconditional numerical value for total solution viscosity.

The terminal ureidopyrimidinone groups supply the association sites. Their urea/pyrimidinone NH donors and carbonyl/ring-nitrogen acceptors can form a self-complementary array of four hydrogen bonds between two UPy units. Joining the two terminal units of one molecule by this noncovalent association closes the ring.

The ether-containing arms provide flexibility and spacing; they are not covalently joined together during ring formation. The ring is therefore a supramolecular conformation of the existing molecule, rather than a new covalent ether macrocycle.

The end groups associate reversibly through a complementary hydrogen-bond array. At low concentration, bringing the two ends of the same molecule together avoids the concentration-dependent cost of finding another molecule, so an intramolecular ring is favored.

For A, increasing concentration permits end-to-end intermolecular association to compete successfully with ring closure. It produces long, reversible supramolecular chains. Increasing chain length and entanglement account for the highly viscous solution without requiring covalent polymerization.

B has more favorably positioned attachment points on its rigid aromatic core. Its arms can close a less strained ring, so intramolecular association remains strongly competitive over the stated range. Predominantly discrete rings do not form the same extended chain network, explaining the retained fluidity. Both compounds can make the same local hydrogen bonds; their different balance of ring strain, preorganization and intermolecular association explains the macroscopic difference.

Surface-treated colloids impose boundary conditions on a nematic liquid crystal, producing director distortions and defects. Bringing particles together can reduce total Frank elastic energy by sharing distortion or defect structures. The interactions are directional: particle–hedgehog dipoles can favor chains, while quadrupolar and confined configurations can favor other arrays. The defects provide orientation-selective bonds rather than an isotropic attraction alone.

Prepare a cell with controlled far-field alignment and particle anchoring. Image textures with a polarizing microscope; use optical tweezers to place two particles at selected separations and orientations, then release them and track their trajectories. Repeating over orientations tests anisotropy before increasing concentration to assemble larger arrays. Compare particles with different anchoring and compare with the isotropic phase to distinguish director-mediated binding from ordinary aggregation. Temperature-dependent viscosity and other surface forces must be accounted for in kinetic comparisons.

The reported two-dimensional nematic colloidal crystals used micrometre confinement and defect-mediated interactions to create ordered particle structures. This motivates the mechanism without implying that arbitrary particles will select the same lattice.^[ref]

A topological defect occurs where the local order cannot be continued smoothly while retaining its surrounding texture. At a nematic disclination core, the director model fails and the orientational order may decrease.

For a planar texture $\mathbf{n}=(\cos \varphi ,\sin \varphi )$,Because $\mathbf{n}\equiv -\mathbf{n}$, half-integer winding strengths are allowed. The original sketches use $\varphi =s\alpha +{\varphi }_0$ to show $s=+1/2,-1/2,+1$, corresponding to director turns $+\pi ,-\pi ,+2\pi$. A radial $+1$ pattern and an azimuthally rotated version have the same winding.

These are planar labels. In unrestricted three dimensions an integer line texture may escape by tilting out of the plane; half-integer lines have a different classification. A planar disclination strength must not be identified automatically with a three-dimensional hedgehog point charge.