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6th Edition of International Conference on

Materials Science and Engineering

March 18-20, 2024 | Singapore

Materials 2023

Eugeny M Pestryaev

Speaker at Materials Science and Engineering 2023 - Eugeny M Pestryaev
Ufa State Petroleum Technological University, Russian Federation

Title : The cage effect and the Frenkel line in the phase diagram


The self-diffusion coefficients and particle lifetimes (t) of the Lennard-Jones liquid in the first coordination sphere of their neighbors were studied by the molecular dynamics simulation for system packing fractions from 0.1 to 0.8. It turned out that the distribution of t is characterized by a wide peak in the region of short times, extending over several decimal orders. It is shown that using a coordination number Z as an argument for the studied characteristics clearly demonstrates emerging and developing the cage effect. The observed self-diffusion-coefficient dependence on the packing fraction is described by the latest self-diffusion theoretically based equation, excluding the system gaseous state, for which this equation was not intended.
The interval Z=5-7, in which the system condensation starts and finishes, coincides with its theoretical value that is necessary to close the cage over the total system. Completing the cage closure leads to the possibility of propagation in such medium of high-frequency transverse elastic waves and, according to the definition, transforms it from a “soft” state to a “solid” one, characterized by appearing the shear viscosity. Locating this transition in the phase diagram with a change in thermodynamic parameters forms a continuous curve, has recently been discovered in experiments by academician V.V. Brazhkin with coauthors and called “the Frenkel line” in honor of the scientist, who has introduced the fruitful cage concept into the liquid theory.
Audience take away:

  • The report presents the physical foundations of the cage effect and its quantitative structural characteristic.
  • This structural characteristic allows to select on the phase diagram a new thermodynamic phase transition in a supercritical fluid, discovered experimentally in 2012.
  • There has always been a long road from knowledge of fundamental regularities to their implementation in some technologies: a researcher who understands the fundamental properties of matter can describe what these properties are and under what conditions they are realized, but he does not give recommendations to process engineers of various profiles on their use.


Dr. E.M. Pestryaev is a molecular physicist by training and received his PhD degree at the Kazan State (Federal) University on studying the structure and dynamics of polymer systems by NMR relaxation. Currently he is an associate professor at the USPTU physics chair. His scientific work focuses on the molecular dynamics simulating the self-diffusion features and their influence on spin-spin magnetic relaxations in condensed media − the long-standing highly specialized problem. He has published more than 40 research articles in Scopus journals, the most of which are without coauthors.