Application of scaling and kinetic equations to helium cluster size distributions: Homogeneous nucleation of a nearly ideal gas

A previously published model of homogeneous nucleation [ Villarica , J. Chem. Phys. 98 , 4610 ( 1993 ) ] based on the Smoluchowski [ Phys. Z. 17 , 557 ( 1916 )] equations is used to simulate the experimentally measured size distributions of He 4 clusters produced in free jet expansions. The model includes only binary collisions and does not consider evaporative effects, so that binary reactive collisions are rate limiting for formation of all cluster sizes despite the need for stabilization of nascent clusters. The model represents these data very well, accounting in some cases for nearly four orders of magnitude in variation in abundance over cluster sizes ranging up to nearly 100 atoms. The success of the model may be due to particularities of He 4 clusters, i.e., their very low coalescence exothermicity, and to the low temperature of 6.7 K at which the data were collected.