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Titel |
Rethinking the first nucleation theorem in atmospheric nucleation |
VerfasserIn |
Matthew McGrath, Kari Lehtinen, Theo Kurtén, Markku Kulmala , Hanna Vehkamäki |
Konferenz |
EGU General Assembly 2011
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Medientyp |
Artikel
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Sprache |
Englisch
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Digitales Dokument |
PDF |
Erschienen |
In: GRA - Volume 13 (2011) |
Datensatznummer |
250052212
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Zusammenfassung |
The first nucleation theorem is a very useful tool in experimental studies of
vapor-liquid nucleation, as it relates the derivative of the nucleation rate with respect
to saturation ratio to the critical cluster size of the system. In other words, one can
measure the nucleation rate of a system at various saturation ratios (holding all other
variables constant), and learn information concerning the structure of the critical
nucleus. This is an invaluable tool, as it's quite difficult to probe the structure of
the critical nucleus directly. It has been well-established that the theorem is accurate
for systems with a single maximum in the free energy profile. In the case of other
systems, however, the case is not so clear. In particular, if there is also a local
minimum on the free energy surface in addition to the global maximum. This is often the
case in ion-induced nucleation, where the addition of multiple neutral molecules (such as
water) serve to stabilize the ion before the free energy barrier to nucleation. It has
been argued that the first nucleation theorem can still be used in this case, either
without modification or with a minor systematic modification, although in-depth
exploration is lacking in the literature.
Through the use of the Atmospheric Cluster Dynamics Code (ACDC), a collection of Perl and
MATLAB scripts, we have solved the system of differential equations for various
fictitious free energy profiles displaying a free energy maximum and one (or zero) free
energy minimums, including one directly applicable for ion-induced nucleation. The
fictitious free energy profiles were produced for single-component water nucleation,
while the ion-induced case is the quasi-one-component water + ion nucleation system. In
addition to the first nucleation theorem, a formula derived by McGraw and Wu was also
used, which is a more general expansion of the first nucleation theorem. Given that
these formulas were both derived under the assumption that only monomers can collide and
evaporate from clusters, and given that this same restriction is not present in explicit
solution of the differential equations deriving the system, both cases were tested by
ACDC (allowing only monomer collisions/evaporations, and allowing all
collisions/evaporations). In order to compare to the experimental case, we explored the
possibility of holding various concentrations constant while computing the derivative of
the nucleation rate with respect to the saturation ratio: the monomer concentration, the
concentration of the cluster at the free energy minimum, and the total concentration of
molecules in the system. We have found that the first nucleation theorem holds true for
the case where there is no free energy minimum (as expected). For a fictitious free
energy profile with one free energy minimum, the first nucleation theorem predicts
incorrect results, regardless of the quantity held constant. For a curve produced by
considering the ion-induced nucleation of water, the first nucleation theorem was found
to give decent results when the concentration of the cluster located at the free energy
minimum was held constant, but not as good of results in the other two cases. These
results have a significant impact on the determination of critical cluster composition
from experiments in atmospheric nucleation. |
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