Influence of size effects on the critical diameter and growth of nanoparticles

Abstract

UDC 541.182The effect exerted by the dependence between the condensation and surface-tension coefficients and the size of an aerosol nanoparticle on its growth and critical diameter is investigated theoretically.Investigation of the characteristic features of transfer processes in aerosol systems with nanosized particles is of interest both for description of the atmospheric phenomena related to the formation and growth of water drops in the atmosphere [1] and for the technological processes where nanoparticles are obtained (or used) [2].It is well known that, when the size of a particle decreases, the processes occurring on its surface begin to play an increasing role. As this takes place, in a number of cases an investigation of the processes in aerosol systems with nanoparticles necessitates taking account of the specific features in the progression of these processes due to the size effects. Thus, for example, the frequent (in phase transitions) assumption that the condensation coefficient is equal to the evaporation coefficient can lead to qualitatively incorrect results in the case of nanoparticles.The saturated vapor pressure over a small particle (drop) depends on its size [1]. The sticking (condensation) and surface-tension coefficients of nanoparticles also become functions of their size [3][4][5]. It should be noted that small particles can arise in a gas phase only at sufficiently high values of the saturation ratio of vapor. The condition of the equilibrium of such particles with a gas phase is determined by the so-called critical size of a particle. In [4], the influence exerted by the dependence between the condensation coefficient and the size of particles on their critical diameter and growth rate was discussed, with the surface-tension coefficient being supposed constant. In the present paper, we consider the joint effect of the condensation and surface-tension coefficients influenced by the size of aerosol nanoparticles on the phase transitions occurring on their surfaces.The particle growth rate v p in vapor condensation can be written as(1)We shall analyze the dependence of j e and j c on the particle size. The flux density of the molecules that evaporate from the surface of a small aerosol particle, with consideration for the Kelvin correction for the saturated vapor pressure over the particle, takes the form(2)According to [6], the evaporation coefficient α e is defined as a coefficient of proportionality between the actual (measured) flux density of evaporating molecules for a flat massive sample and the greatest possible, during evaporation into vacuum, flux density, which is equal to P e /(2πmkT s ) 1 ⁄ 2 . In other words, the evaporation coefficient is a measure of the deviation of an actual evaporation rate from the greatest possible one for a flat massive sample. With such a definition, the evaporation coefficient is independent of the particle size (the size dependence of the evaporation rate is taken into account by the exponential term in (2), which describes, according to the Kelv...

Predicting the influence of particle size on the glass transition temperature and viscosity of secondary organic material

“…Surface tension itself increases with decreasing particle diameter below the Tolman length 50,51 . Furthermore with decreasing particle diameter, the deliquescence relative humidity and efflorescence relative humidity increases [52][53][54] , the equilibrium hygroscopic growth factor decreases 55 , the condensation coefficient of the gas molecule to the particle surface decreases 56 , and liquid-liquid phase separation is suppressed [57][58][59][60] . Virtanen et al 23,61 showed that the bounce factor of organic particles produced by OH dominated oxidation of pine emitted volatile organic compounds sharply decreases for particles with D < 30 nm , but not for solid ammonium sulfate particles.…”