Rate Constants and Sticking Coefficients for H₂ and He Obtained by Analysis of Agglomeration in a Nozzle Beam

Cluster–cluster reaction rate constants are obtained from measurements of coalescence in nozzle-beam expansions. Coalescence is described by the Smoluchowski equations, modified to accommodate changes in volume and temperature. The asymptotic form of the cluster size distribution can reveal the scaling of the second-order rate constants K_jk with the sizes of colliding particles. Scalings derived in the past are demonstrably incorrect and physically unjustifiable. Here, we use the physically reasonable scaling, K_jk = K₁₁j^μk^μ, to study H₂ coalescence in a nozzle beam. Experimental size distributions fit the predicted asymptotic form, N_k = Ak^ae^−bk, very well, with deviations identifying magic numbers. We obtain the base agglomeration cross section K₁₁ and the parameter μ, and thus all the rate constants, for H₂. By comparing with products of geometric cross section and relative velocity, we find sticking coefficients. Experimental results for a nozzle-beam expansion of He are analyzed similarly, to yield K₁₁ and μ, and hence sticking coefficients, for He. These are compared to those for H₂.