Studies on the Formation of Topological Isomers by Statistical Methods

To improve the statistical synthesis of topological isomers, the factors which determine the amount of threading of linear chain molecules in macrocyclic rings were studied in detail. Polymeric rotaxanes were prepared by statistical threading of polyethylene glycols) in “crown polyethers”. The compounds were mixed and heated, and the equilibrium was “frozen” by polymerization of the chains to polyurethanes by adding naphthalene-1,5-diisocyanate. The amount of threaded rings was determined after selective separation of the components on silica gel. The effects of the molar ratios of rings to chains, length of chain, radius of the ring, volume of the system, and temperature on the amount of threading were studied. Based on statistical consideration of ratio of reactants and volume of the system, and on geometrical factors, the following mathematical expression was derived to show the effect of these factors on the amount of threading: N = k[m_cm_g(1 - e^-n_e/πng)n_en_g^βθ]/V where N is the number of threadings, m_e and m_g are the number of moles of rings and chains respectively, ne and ng are the number of atoms in rings and chains, V is the total volume, and is the threading angle, which depends on the radius of the ring (r) and diameter of the chain end (d) and is determined by cos θ= d/2r. The constants β and k which suit the results are β = 1.3 and k = 0.195. There was good correlation between this mathematical model, the experimental results, and molecular models imitating the ring-chain threading system. The optimal conditions found for the threading system was utilized for the preparation of [2]-[ω,ω′-di(O-trityl)poly(ethylene glycol) 400]-[dibenzo-58.2-crown-19.4]rotaxane in relatively high yield (15%). Similar yield was obtained by polymerizing ethylene oxide by the di(potassium alkoxide) derivative of tetra(ethylene glycol) in the presence of “crown” polyether. Chromatographic and spectral evidence, as well as hydrolysis of the blocking trityl groups, was used to prove the structure of the rotaxane. The thermal decomposition of the rotaxane was investigated at 130-190 °C. The following equilibrium was found to exist: rotaxane ring ⇌ chain (k, k′), and the reaction constants were determined. The stability of the rotaxane was explained, taking into consideration the data obtained for the heat of decomposition (9.5 kcal/mol) and the activation energies of the decomposition and threading processes (15.9 and 3.4 kcal/mol, respectively). The higher activation energy needed for the decomposition was explained by the dipole-dipole interactions which exist between the ethylene oxide units in the threaded chain and those in the ring.