Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2022 / Paper 1 / Section A(iii) / 5

Use consistent units for the Gibbs free energy:Then $\Delta G^{\circ }=-RT\ln K$ givesThis is a dimensionless thermodynamic equilibrium constant defined through activities. For an ideal dilute $1:1$ association, the numerical concentration association constant is about $4.53\times 10^3{\mathrm{M}}^{-1}$ when concentrations use the $1\mathrm{M}$ standard state. Both favourable enthalpy and positive entropy favour association here; association need not always have a negative entropy change because solvent release can outweigh the loss of translational freedom.

Cyclodextrins are truncated-cone-shaped hosts that form host–guest complexes. Their hydroxyl-rich exterior interacts favourably with water, while the internal cavity is relatively nonpolar and can accommodate a suitably sized organic guest. The six-, seven- and eight-unit rings have different cavity sizes, so shape and size selectivity matter. Binding can involve London dispersion forces, displacement of cavity water and changes in solvation; no covalent modification of the guest is necessary.

An odorous organic guest can be included in the cavity, decreasing its free concentration and hence its tendency to enter the vapour phase. The same inclusion chemistry can increase the apparent aqueous solubility of a poorly soluble compound, and reversible association allows release when conditions or concentrations change. In a separation, guests with different association constants partition differently between free and bound states; a suitably immobilized host can therefore act as a selective stationary phase.

The unifying mechanism is reversible molecular inclusion in a size-selective cavity. These are chemical explanations of binding and partitioning. Biological action, therapeutic efficacy and physiological delivery mechanisms are outside the present nonbiology scope.

The gas-phase attraction is a cation–π interaction. The positively charged ion interacts with benzene's electron distribution and polarizes the aromatic molecule. An orientation above the ring face allows stabilization without a conventional covalent bond. A modest association constant reflects the balance of that attraction against the entropy cost of joining two independent species, at the stated gas-phase standard state.

In water, a small ion such as $\mathrm{L}{\mathrm{i}}^{+}$ is strongly solvated. Forming a direct benzene complex requires rearranging or losing favourable ion–water contacts; benzene is also solvated, and the solvent screens electrostatic interactions. The relevant solution free energy therefore includes desolvation and solvent reorganization, not just the attractive energy of the isolated pair. The gas-phase association constant cannot be transferred to water without changing this thermodynamic cycle and the standard states. The interaction is not forbidden in solution, but it need not give appreciable direct complexation under the specified conditions.

The receptor is a triazolophane with a relatively rigid central cavity. Its inward-facing triazole and phenylene C–H groups act cooperatively as hydrogen bond donors to an anion. The supplied preference is $\mathrm{C}{\mathrm{l}}^{-}>\mathrm{B}{\mathrm{r}}^{-}\gg {\mathrm{F}}^{-}>{\mathrm{I}}^{-}$, so it is not a simple ranking by charge density or basicity.

Chloride has the best fit for several favourable C–H···anion contacts simultaneously; bromide is close enough in size to retain strong binding. Fluoride is too small to engage the whole donor array optimally, and its desolvation penalty can further oppose binding in solution. Iodide is too large for the cavity and cannot sit in the same favourable geometry. Molecular preorganization reduces the conformational penalty for binding a matched guest, but makes the cavity less adaptable to mismatched ones.

The exact solvent is not specified in this question, so a quantitative hydration argument would be unwarranted. The structure and observed nonmonotonic order support size complementarity plus cooperative C–H hydrogen bonding, with solvation modifying the measured constants. The original receptor study experimentally demonstrated halide size selectivity and tunability through the phenylene substituents.^[ref]