Statistical Thermodynamics of Two-Dimensional Fluids of Solid Nanoparticles
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Statistical Thermodynamics of Two-Dimensional Fluids of Solid Nanoparticles Liudmila A. Pozhar and John Maguire Air Force Research Laboratory, Materials and Manufacturing Directorate, Polymer Materials Branch (AFRL/ MLBP) 2941 Hobson Way, Wright-Patterson Air Force Base, OH 45433-7750, U.S.A. ABSTRACT The second virial coefficient-based statistical thermodynamics of a diluted fluid of rigid particles of regular polygonal shape is discussed. Analytical expressions for the second virial coefficient, surface tension, isothermal compressibility and isothermal speed of sound are derived in this approximation. The obtained results provide analytical guidelines for numerical simulations and modeling studies of two-dimensional (2D) particulate fluids (thin films) widely used in processing of model (nano)composite materials and other technological processes.
INTRODUCTION Particulate fluids constitute an inevitable component of almost any technological process in many industries, from composite nanomaterial development, mineral and energy carrier processing to handling wheat harvest, drug packaging and delivery, lubricant development and use, waste treatment, water and air purification and pollutant separation, etc. In recent years, thermodynamic properties of particulate fluids receive significant attention due to an increasing demand for development of processes, technologies, materials and media that are environmentally clean and at the same time, affordable. Many of particulate fluids and their mixes with proper fluids demonstrate complicated interactions between their constitutive particles caused by friction of the particles during of their motion that leads to charging of individual particles. Depending upon the nature of the proper fluids in the mix, the entire systems may or may not have to be treated as a system of charged particles. In many cases these mixes include such fluids as water, that act as a medium that takes care of the charge re-distribution, so that a solid particle in the mix is not charged. In such cases the solid particles only interact with each other when they collide. At normal conditions, the kinetic energy of the colliding hard particles is small, collisions do not change the shape or structure of the particles and thus can be considered as elastic. The interparticle interaction potential u(r1,r2) in this case is that specific to classical rigid bodies, ∞ , | r1 − r2 |≤ S (r1 , r2 ); u (r1 , r2 ) = 0 , | r1 − r2 |≤ S (r1 , r2 ),
(1)
where r1 and r2 denote positions of the centers of mass of the interacting particles 1 and 2, the symbol |…| signifies the absolute value of a vector, and the scalar quantity S depends upon the positions and shape of the interacting particles. The potential (1) takes the simplest form for spherical particles, in which case it is called the hard (or rigid) sphere potential, with S equal to the particle diameter d, S=d. The collision geometry of hard classical spheres is simple and leads to simple statistical thermodynamics known since Boltzmann. Indee
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