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"Density functional theory of size-dependent effects in thermodynamics of droplets on neutral and charged nanoparticles"

Dr. Prof. A.K. Shchekin

Size-dependent effects in thermodynamics of droplet formation on wettable uncharged and charged solid particles are
related to the nonuniformity of the droplet provided by overlapping surface layers the solid core-liquid film and
the liquid film-vapor. The overlapping can be thermodynamically described in terms of competition between the capillary
and the disjoining pressure as contributions to the chemical potential of a condensate molecule in the droplet which
can phenomenologically be taken the same as for flat thin liquid films [1,2]. The disjoining pressure is created by
molecular forces in small volumes and can be modified by presence of long-range electrical forces.

In the case of uncharged solid cores, the attempts to compute the disjoining pressure in the droplet on a molecular
level were undertaken more than ten years ago by Napari and Laaksonen [3] and by Bykov and Zeng [4,5] with the help
of the nonlocal density functional theory (DFT) for fluids with the Lennard-Jones molecular potential. îÅrÅ we
would like to extend the study by consideration of the effect of molecular interactions of the condensate molecules
with the solid core jointly with the effect of central electric field in the case of charged core. A similar problem
had been formulated for ion-induced nucleation by Kitamura and Onuki [6], and we made a development of it recently for
condensation cores of molecular size [7,8]. However, the situation in the case of nanosized and larger condensation
cores has its own specificity. It is associated with increasing the disjoining pressure with the size of the core
and its possible interplay with the electric field of a charged core. Increasing the size of the cores also establishes
limits for complete wetting and affects the work of wetting.

We report here the results of numerical study of the size-dependent effects for the chemical potential, disjoining
pressure and work of droplet formation of a small droplet with solid insoluble core. The study has been performed
within the square-gradient DFT [9]. The Lennard-Jones fluid with the Carnahan-Starling model for the hard-sphere
contribution to intermolecular interaction in liquid and vapor phases and interfaces has been used for description
of the fluid condensate. The intermolecular forces between the solid core and condensate molecules have been taken
into account with the help of the Lennard-Jones part of the total molecular potential of the core. The influence
of the electric charge of the particle has been considered under assumption of the central Coulomb potential in the
fluid with the dielectric permittivity depending on local condensate density. The condensate density profiles and
equimolecular radii for equilibrium droplets at different values of the condensate chemical potential have been
computed in the cases of an uncharged solid core with the molecular potential, a charged core without molecular
potential, and a core with joint action of the Coulomb and molecular potentials. The capillary and disjoining
pressures in the droplet and electrostatic contributions to the condensate chemical potential have been found
and compared with the predictions of classical thermodynamics and thermodynamics of mesoscopic droplets [1,2].
With the help of the found dependence of the condensate chemical potential in droplet on the droplet size, the
energetic characteristics of nucleation on uncharged and charged particles have been computed as functions of vapor
supersaturation and core size.

This work was supported by the Russian Foundation for Basic Research grant 16-03-00281 mol-a.


[1] F.M.šKuni, A.K.šShchekin, A.I.šRusanov, B.šWidom, Adv. Colloid Interface Sci. 65, 71,1996.
[2] A.K. Shchekin, T.S. Podguzova, Atmospheric Research 101, 493, 2011.
[3] I.šNapari, A.šLaaksonen, J.šChem. Phys. 119, 10363, 2003.
[4] T.V.šBykov, X.C.šZeng, J. Chem. Phys. 117, 1851, 2002.
[5] T.V.šBykov, X.C.šZeng, J.šChem. Phys. 125, 144515, 2006.
[6] H. Kitamura, A. Onuki, J. Chem. Phys. 123, 124513, 2005.
[7] A.K. Shchekin, T.S. Lebedeva, D.V. Tatyanenko, Colloid J. 78, 553, 2016.
[8] A.K. Shchekin, T.S. Lebedeva, D.V. Tatyanenko, Fluid Phase Equilib. 424, 162, 2016.
[9] A.K. Shchekin, T.S. Lebedeva, J. Chem. Phys., 146, 094702, 2017.