Attempts at modeling this important and still enigmatic process also appeared
rather long ago. Here we avoid the long history of this problem and cite only the
last models that appeared in the twenty-first century (Stolzenburg et al. 2005 ;Yu
and Turko 2001 ; Anttila et al. 2004 ;Kerminenetal. 2004 ; Korhonen et al. 2003 ,
2004 ; Lehtinen and Kulmala 2003 ; Grini et al. 2005 ; Lushnikov et al. 2008 , 2010 ;
Lushnikov 2010a , b ). Earlier citations can be found in these works. All models
(without exception) started from the commonly accepted point of view that the
chemical reactions of trace gases are responsible for the formation of nonvolatile
precursors, which then give life to subnano- and nanoparticles in the atmosphere.
In their turn, these particles are considered as active participants of the atmospheric
chemical cycles leading to particle formation (see, e.g., Janson et al. 2001 ).
Many facts concerning the natural background aerosols have been well estab-
lished. The major features of the phenomenon can be summarized as follows:
The smallest (nanometer) aerosol particles form by nucleation of low volatile
vapors resulting from intra-atmospheric chemical and photochemical transfor-
mations. The complete chemical cycles responsible for this very complicated
process are not yet fully known, and its output is therefore characterized by the
volume productivity I.t/ of the cycle: the number of molecules produced in a
unit volume at a time. The source productivity is likely a periodic function of
time (diurnal cycle).
Very often observed size spectra reveal a multimodal (mostly trimodal) structure:
a peak at 10-25 nm (nucleation or highly dispersed mode) and two submicrom-
eter peaks at 25-100 nm and at 100-200 nm (Aitken and submicrometer modes)
(Kulmala et al. 2004 and citations therein).
The spontaneous nucleation of low volatile vapors is believed to give rise to the
production of highly dispersed particles, whose number concentration is strongly
dependent on the vapor concentration level.
Submicrometer particles are often suspected to result from aging smaller par-
ticles as a result of their growth by condensing the molecules of low volatile
substances. On some occasions the submicrometer particles can be transported
from somewhere else.
As is seen from this list, the theoretical modeling of the particle formation-
growth process is not a simple task: the point is that the process envelops a very
wide range of particle sizes: from nanometers to parts of micrometers (three decimal
orders) and masses (nine decimal orders). The respective kinetic processes proceed
in various regimes: from free molecular to continuous ones, and the characteristic
time scales are also stretched from minutes to hours and even weeks. These facts
require one to seek for some simplifications or to sacrifice a part of the picture. For
example, the most widespread of models in the past described the process in terms
of interacting particle modes, each of which was characterized by its size interval
and the number concentration. The time evolution of these values was described
by a set of differential equations. These equations included the sources, the sinks
of the particles, and the terms describing the aerosol processes. The quality of the
models depended on the number of modes taken into account and the way of their
introduction. The simplest results were obtained for a single-mode case.