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We here present a statistical model of hydrogen bond induced network structures in liquid alcohols. The model generalises the Andersson-Schulz-Flory chain model to allow also for branched structures. Two bonding probabilities are assigned to each hydroxyl group oxygen, where the first is the probability of a lone pair accepting an H-bond and the second is the probability that given this bond also the second lone pair is bonded. The average hydroxyl group cluster size, cluster size distribution, and the number of branches and leaves in the tree-like network clusters are directly determined from these probabilities. The applicability of the model is tested by comparison to cluster size distributions and bonding probabilities obtained from Monte Carlo simulations of the monoalcohols methanol, propanol, butanol, and propylene glycol monomethyl ether, the di-alcohol propylene glycol, and the tri-alcohol glycerol. We find that the tree model can reproduce the cluster size distributions and the bonding probabilities for both mono- and poly-alcohols, showing the branched nature of the OH-clusters in these liquids. Thus, this statistical model is a useful tool to better understand the structure of network forming hydrogen bonded liquids. The model can be applied to experimental data, allowing the topology of the clusters to be determined from such studies.

A statistical model of hydrogen bond networks in liquid alcohols