Structure and Energetics of Poly(Ethylene Glycol) Cationized by Li +,Na +,K + and Cs + : A First-Principles Study

Density functional theoretical methods, including several basis sets and two functionals, were used to collect information on the structure and energetic parameters of poly(ethylene glycol) (PEG), also referred to as poly(ethylene oxide) (PEO), coordinated by alkali metal ions. The oligomer chain is found to form a spiral around the alkali cation, which grows to roughly two helical turns when the oligomer size increases to about the decamer for each alkali ion. Above this size, the additional monomer units do not build the spiral further for Li⁺ and Na⁺; instead, they form less organized segments outside or next to the initial spiral. The distance of the first layer of coordinating O atoms from the alkali cation is 1.9–2.15 Å for Li⁺, 2.3–2.5 Å for Na⁺, 2.75–3.2 Å for K⁺ and 3.5–3.8 Å for Cs⁺ complexes. The number of O atoms in the innermost shell is five, six, seven and eleven for Li⁺, Na⁺, K⁺ and Cs⁺. The collision cross sections with He increase linearly with the oligomer to a very good approximation. No sign of leaning towards the 2/3 power dependence characterizing spherical particles is observed. The binding energy of the cation to the oligomer increases up to polymerization degree of about 10, where it levels off for each alkali-metal ion, indicating that this is approximately the limit of the oligomer size that can be influenced by the alkali cation. The binding energy–degree of polymerization curves are remarkably parallel for the four cations. The limiting binding energy at large polymerization degrees is about 544 kJ mol⁻¹, 460 kJ mol⁻¹, 356 kJ mol⁻¹ and 314 kJ mol⁻¹ for Li, Na, K and Cs, respectively. The geometrical features are compared with the X-ray and neutron diffraction data on crystalline and amorphous phases of conducting polymers formed by alkali-metal salts and PEG. The implications of the observations concerning collision cross sections and binding energies to ion mobility spectroscopy and mass spectrometry are discussed.