How does hydrogen bond network analysis reveal the golden ratio of water-glycerol mixtures?

Properties of water-glycerol mixtures depend closely on the water/glycerol ratio. Around the 30 mol% glycerol concentration mark, the so-called golden ratio of water-glycerol mixtures, several of the mixture's properties have observed maxima or minima, without a clear fundamental explanation. In this work, a series of molecular dynamics simulations have been performed over a wide range of water-glycerol concentrations to analyze the intermolecular hydrogen bond (H-bond) network. The collected values from simulations are justified from both a probabilistic model of H-bonding and from observing the dynamic behavior of each type of H-bonds. The populations of H-bonds that exist at a given concentration of glycerol are largely governed by the probability of one oxygen atom randomly associating with another oxygen atom. However, the H-bonds that glycerol oxygen can form are dependent on the H-bonds that are formed by the other intramolecular glycerol oxygen. Based on the dynamic analysis of each type of H-bonds, there are deviations from randomly associating with another oxygen. Water preferentially donates a hydrogen to a glycerol than to another water molecule. Yet, glycerol has a near-equal likelihood for donating a hydrogen to either another glycerol or a water. This has an effect of increasing the number of H-bonds between water and glycerol molecules and decreasing H-bonds between two water molecules. A maximum contribution of H-bonds between water and glycerol occurs around 30 mol% glycerol which is a concentration where several of the mixture's properties have an observed maxima or minima.