A statistical model of hydrogen bond networks in liquid alcohols

Abstract

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.

Size distribution of associated clusters in liquid alcohols: Interpretation of simulation results in the frame of SAFT approach

“…The cluster-size distributions discussed in this work correspond to "fraction of clusters of size n from the total amount of clusters"; in agreement with Sillrén et al 33 we use for it symbol r(n). The size of clusters is considered irrespective of their topology, thus all tetramers shown in Figure 1 contribute to the same value, n = 4.…”

“…13 The mean values at T = 300 K for propanol and butanol are approximately 25% higher compared with the values of Ref. 33. Although the distribution characteristics presented in Table I are not convincing, one can again take notice of rather close values for the longer alcohols.…”

“…73,74 The cluster-size distribution function for ethanol at T = 300 K is shown in Figure 7. The simulated distribution (crosses) is compared with three models -2B association scheme of SAFT (solid black line), 3B scheme (dashed red line), and with the model suggested recently by Sillrén et al 33 (dashed-dotted blue line). Within the last model, the fraction of clusters of size n is given by recurrent formula…”

“…Three different tetramers composed of such associating molecules are also shown (the green circles denote existing hydrogen bonds). The greek letters correspond to the notation used by Sillrén et al 33 -α denotes the molecules not participating on hydrogen bond formation, β denotes the "root" molecules of particular clusters (the molecules with nonbonded hydrogen site), γ stands for "leafs" (end molecules of particular branches) and δ denotes the internal groups. The subscripts in case of roots and internal groups denote the number of bonded donors, so roots of true trees β 1 are distinguished from U-like associates β 2 and the standard internal groups δ 1 from branching nodes δ 2 .…”

“…Several recent as well as classical studies were aimed to analyze the size and topology of associated species. 11,[25][26][27][28][29][30][31][32][33] The thermodynamic description of systems containing associating compounds represents a difficult task, especially in the case of mixtures of associating and non-associating components (e.g., alcohol-alcane) or systems which experience the cross-association despite the particular components alone do not associate (e.g., chloroform-acetone). 34 Among several approaches suggested to treat the behaviour of associating systems, the statistical association fluid theory (SAFT) of Wertheim [35][36][37][38] gained a prominent position and was incorporated into a family of equations of state.…”