Layering Phase Transition in a Liquid Solution with Cross Hydrogen Bonds: Bond Number Density as the Second Order Parame
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Layering Phase Transition in a Liquid Solution with Cross Hydrogen Bonds: Bond Number Density as the Second Order Parameter G. A. Lyakhova, I. A. Shcherbakova, and M. A. Shermenevaa, b, * a
Prokhorov General Physics Institute of the Russian Academy of Sciences, Moscow, 119991 Russia bNational Research Nuclear University MEPhI, Moscow, 115409 Russia *e-mail: [email protected] Received April 16, 2020; revised April 16, 2020; accepted April 20, 2020
Abstract—An isobaric equation of state of a binary solution with hydrogen bonds is derived using the thermodynamic grid model. Temperature dependences of the molecular and bond concentrations are calculated. The dependences demonstrate phase transitions, for which both concentrations serve as the order parameters. It is shown that this bicomponent can give rise to new properties of the solution. In particular, there is a threshold hydrogen bond energy over which condensation of hydrogen bonds occurs in a certain range of molecular concentrations. DOI: 10.3103/S1541308X20030139
1. INTRODUCTION Physics of liquid solutions has a wide field of application ranging from materials science to biomedicine. The main stimulus for its development is the crucial role played by aqueous solutions of various molecular compositions in biological processes. The predictive ability of the existing theory of liquids, even of those with a homogeneous structure, is currently poorer than that of the solid state theory. Objectively, this is because stochastic phenomena carry much more weight in liquid media. Construction of the theory faces even more difficulties when liquid media with the dynamic structure are concerned. The most illustrative example is water and aqueous solutions with short-lived hydrogen bonds between molecules. Physics of water and aqueous solutions has collected a great deal of experimental data and has developed a number of theoretical approaches to their interpretation (see, for example, [1, 2]). Some of these approaches employ advanced mathematical methods (see, for example, [3]). The goal of this work is to get a better insight into the thermodynamic theory of solutions with intermolecular hydrogen bonds. Our approach is based on the grid model (see, for example, [4]) of a liquid medium, the statistical substantiation of which was outlined in [5]. The work was done in continuation and furtherance of the theoretical program formulated in [6]. 2. THERMODYNAMIC MODEL Let the binary solution with the total (and constant) number of molecules N = H + h + G + g (at con-
stant pressure) consist of molecules of two types, “hosts” and “guests”. We assume that each molecule can be either free or linked by the hydrogen bond (HB) to a molecule of the other type. Let the numbers of free molecules be H and G, and the numbers of bound molecules be h and g. In compliance with the above assumption, h = g = B, where B is the number of HBs. In our generalization of the grid model, the intermolecular interaction energy E is
(
E = − 1 1 uHH H 2 + uGGG 2 + uhhh2 + ugg g
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