Stability

Hydrogen bonds of cellulose molecules were discussed using quantum mechanics. In other words, the picture is that hydrogen bonding is an exchange force between two oxygen atoms due to proton vibrations. The formation of hydrogen bonds between the hydroxyl groups of cellulose makes the energy of the system small and stable depending the amplitude of proton transfer. When the amplitude is A, the proton oscillates at a frequency of 2A/ħ in the case of O2-O6 intramolecular hydrogen bond where the hydrogen bond is symmetrical; if the bond is asymmetrical, as in the case of O3-O5 intramolecular hydrogen bond, the amplitude is smaller than A. In the case of O6-O3 intermolecular hydrogen bond, the two previous intramolecular hydrogen bonds must be considered simultaneously. In the case of a series of three such hydrogen bonds, the energy of the bonding state may be smaller or larger than that of the single hydrogen bond, but the total system energy is smaller than that of the single hydrogen bond. If hydrogen bonding is a two-body interaction, three-body interaction, etc., the strength of the system should be expressed by a power series expansion. However, empirically, it is reasonable to consider hydrogen bonding as an exchange force since it is generally correlated with the number of hydroxyl groups. It is possible to determine the amplitude from the infrared absorption measurement of cellulose.