The Molecular Physics of Chain Clusters Boris Sedunov Professor Russian New University Moscow

Clusters around us Clusters are as multiple as chemical compounds, in spite of their small bond energy; Clusters in Space give origin to Galactic clouds; Water clusters produce clouds above us and transfer to us the smell of food; In supercritical fluids at a critical density clusters join together and merge, thus providing transition between gaseous and liquid states; Clusters influence properties of technological gases, why should be studied with a due care!

Water Clusters – the seeds of clouds Clear blue sky areas between clouds are filled with small invisible Water Clusters. Visible clouds contain drops of Water with diameter exceeding 1 mkm.

A sudden discovery At the 2 nd ATINER Conference on Physics the author declared that the Physics of Clusters benefits from the computational analysis of precise data, contained in the NIST database for Thermophysical Properties of Fluids. By this way a unknown type of Chain Clusters was suddenly discovered. They have been found in many gases, such as Noble and polar gases, CO 2, N 2, F 2, Alkanes, ….

The investigated pure gases with 1D Chain Clusters Noble gases: Helium; Neon; Argon; Krypton; Xenon Alkanes: Methane; Ethane; Butane; Propane No polar molecular gases: Carbon Dioxide; Nitrogen; Fluorine Polar gases: Water vapor; Heavy Water vapor; Ammonia; Hydrogen Sulfide; Dinitrogen Monoxide; Sulfur Dioxide.

A domination of Chain Clusters The Chain Clusters are 1D polymer-like linear chains of n molecules possessing (n – 1) pair bonds between them. They dominate over 3D Clusters at densities reaching the fifth of the critical density and at temperatures over the middle point T m between the triple T tr and critical T cr points. The domination of Chain Clusters in such a wide zone of densities and temperatures is a generous present of Nature opening possibilities to investigate the clusters’ formation physics!

Chain Clusters’ domination zone for Water vapor

Clusters’ properties extraction from precise experimental data The gas potential energy U = (E(T, P) – E(T, 0)), where E(T, P) and E(T, 0) are internal energies of real and ideal states of a gas at a temperature T. Its positive density W = (-UD) divided by second power of the monomer fraction density D m, is the function W 2+ (D m ) = (-UD) / D m 2 to be expanded in series by D m. The zero pressure limit of it gives the pair bonding coefficient W 2. We will analyze W 2+ / W 2 - the no dimensional function of D m.

The W 2+ (D m )/W 2 function in CO 2 at 300 K is highly nonlinear The inversely proportional function W 2 / W 2+ is linear! This linearity is the unknown before law of Nature! The key to discovery

The geometric progression law The linear part of graph for W 2 / W 2+l may be written as: W 2 / W 2+l = 1- V u (T) D m.(1) The inversely proportional function W 2+l / W 2 corresponds to the equation (2): W 2+l / W 2 = (1 - V u D m ) -1 (2) and looks like a geometric progression sum. The common ratio of the geometric progression, V u D m, determines an infinite row of equilibrium coefficients: W n = W 2 (V u D m ) n-2

Properties of Chain Clusters

The W 2 / W 2+ vs D m in Krypton 153 K 300 K 501 K 750 K

The correlation of V u (solid line) and 4C 2 in Krypton TBTB

The nature of the pair interaction coefficient C 2 (T) The system of series expansions of pressure and density by D m, derived by Sedunov (2008) and confirmed for many real gases, looks like: P = RT ∑ C n D m n, D = ∑ n C n D m n, C 1 = 1. The second equilibrium coefficient C 2 (T) is the pair interaction coefficient for dimers. - C 2 = B – the second virial coefficient.

3D Clusters’ contribution ∆W 2+ (thick line) in W 2+ (thin line) in Xe

An averaged number of Xe particles in 3D Clusters at T = 280 K

Conclusions The equilibrium thermophysical properties analysis reveals the structure of clusters in real gases. The thermophysical data series expansion by monomer fraction density discovers 1D Chain Clusters. The Chain Clusters dominate in a wide and important for science and practice T-D zone. The Chain Clusters’ characteristics obey to the geometric progression law. The knowledge of the Chain Clusters’ parameters opens ways to the 3D Clusters investigation.

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