Temperature dependent network stability in simple alcohols and pure water: The evolution of Laplace spectra

Abstract

A number of computer-generated models of water, methanol and ethanol are considered at room temperature and ambient pressure, and also as a function of temperature (for water and ethanol), and the potential model (for water only). The Laplace matrices are determined, and various characteristics of this, such as eigenvalues and eigenvectors, and the corresponding Laplace spectra are calculated. It is revealed how the width of the spectral gap in the Laplace matrix of H-bonded networks may be applied for characterising the stability of the network. A novel method for detecting the presence percolated network in these systems is also introduced. these studies of networks where large systems of interactions are mapped into graphs, vertices and edges are usually recognized as the primarily building blocks. Given a graph we can associate several matrices which record information about vertices and how they are interconnected.Over the past several years considerable attention has been focused on studying complex networks. A large number of concepts have been introduced for classifying network structures, for example degree distribution, path length, clustering, percolation, the small world property, spectral density of graph, ring structures, etc. During the last years it has become clear that the Laplacian eigenvalues and eigenvectors play an important role in revealing the multiple aspects of the characteristics of network structure and dynamics, like spanning trees, resistance distances and community structures [11][12][13][14][15][16][17][18][19][20][21][22].There are several example of application of network science concepts in chemistry and physical chemistry, too [23][24][25][26][27][28][29][30][31][32][33]. Hydrogen-bond (HB) connectivity and strength and directionality influence the anomalous properties of water and other H-bonded liquids and liquid mixtures. It is widely accepted that water prefers to form a complicated three-dimensional percolated network [34][35][36]. On the other hand, bulk methanol and ethanol form (mostly) chain-like clusters [38,39].Recently we have applied well known graph theoretical concepts for revealing basic units of the network structure in liquid water at room temperature, in water-methanol mixtures at different temperatures [40,41], and in formamide [42]. We found that methanol molecules prefer to form non-cyclic entities, whereas water molecules favour to build rings and the number of cyclic entities in the mixtures is increasing as the temperature is decreasing.Several authors have already used the properties of the spectral density of adjacency and/or Laplace matrices calculated for H-bonded networks, in order to characterise more deeply the Hbonded structure in pure liquids and liquid mixtures [24][25][26][27][28][29][30]33] . In the current study, we investigate spectral properties of the hydrogen bond network in liquid water, as well as in simple alcohols methanol and ethanol at different temperatures. At present, we focus mainly on producing some metrics that could provid...

Properties of Hydrogen-Bonded Networks in Ethanol–Water Liquid Mixtures as a Function of Temperature: Diffraction Experiments and Computer Simulations

“…It has already been shown that the Laplace spectra 57 − 67 of H-bonded networks are a good topological indicator for monitoring the percolation transition in liquids. 68 Several authors have studied the relationship between the eigenvector corresponding to the second smallest eigenvalue (λ 2 ) and the graph structure; well-documented reviews can be found in the literature. 58 , 62 , 65 More details are available in the Supporting Information .…”

“…The low λ values (up to 0.3) are enlarged at the bottom. Spectra of the pure constituents can be found in ref ( 68 ). According to the topology of the H-bonded network, two cases can be distinguished in connection with the Laplace spectra: (1) For liquids whose molecules form a 3D percolated network, a well-defined gap can be detected at low eigenvalues.…”

“…Pure water falls into the first category, while pure liquid ethanol belongs to the second one. 83 Concerning the mixtures, the existence of the gap mentioned above (c.f. Fig.…”

Molecular aggregation in liquid water: Laplace spectra and spectral clustering of H-bonded network

“…This network-specific approach to characterize the connectivity in Hbonded systems in depth have been already utilized in earlier studies of water and aqueous solutions. [13][14][15][16][17][18][19][20][21] In our recent study, on pure water forming a 3D space filling percolated network, a well-defined gap was detected in the spectrum at low eigenvalues, and this gap becomes smaller as temperature increases. [20] This work focuses on revealing the properties of the Laplace spectra for TIP4P/20005 water model [22] to find connection with the structural features of real liquid by means of utilizing the spectral clustering method [23][24][25][26][27][28][29][30][31][32].…”

“…[13][14][15][16][17][18][19][20][21] In our recent study, on pure water forming a 3D space filling percolated network, a well-defined gap was detected in the spectrum at low eigenvalues, and this gap becomes smaller as temperature increases. [20] This work focuses on revealing the properties of the Laplace spectra for TIP4P/20005 water model [22] to find connection with the structural features of real liquid by means of utilizing the spectral clustering method [23][24][25][26][27][28][29][30][31][32]. This approach is based on the eigenvector decomposition of a Laplacian matrix and treats the data clustering as a graph partitioning problem without making any assumption of the form of the data clusters.…”