Model for Production of Hydrogen Clusters

Abstract

RECENTLY Floyd and I reported1 the generation of water clusters of the type H+(H2O)n from the surface of ice films by low energy electron bombardment and subsequent mass spectrometric analysis and proposed a model utilizing the excess energy of the ionized fragment H+. The interpretation of the data permitted the separation of two mechanisms contributing to the cluster-crystal attraction E(n), namely the ion-induced dipole field and the neutral-neutral binding, assigned to hydrogen bonding in the case of water. The former decreases with increasing cluster size and the latter increases, such that a minimum energy occurs for a particular value of n. Although the induced dipole field is generally regarded as “long range”, the contribution of nearest neighbours to the summation over all lattice points is very large, such that the minimum in E(n) occurs at a value of n very close to the number of nearest neighbours for a lattice point on the surface of the crystal, that is n=5 for a cubic lattice, n=8 for a face-centred cubic lattice. We believe, therefore, that the observed distribution of cluster size in such experiments is determined by the lattice properties and not by a gas kinetic theory, based on the minimization of free energy; for the vacuum levels used (≳10−8 torr) there is no mechanism whereby gaseous ion clusters may arrive at an equilibrium size distribution. Water is not an ideal molecule with which to establish these concepts firmly, for the crystal structure is complex and the presence of a permanent dipole moment complicates calculation of E(n) from first principles. Solid hydrogen, however, is more amenable to analysis and results of similar experiments by Clampitt and Gowland2 are used here as an additional test of the model, in which dissociative ionization of H2 results in a family of (the type H+(H2)n. The requirement of excess proton energy to provide a cluster kinetic energy adequate to overcome the binding energy for the nth cluster, E(n), is again satisfied and, as in the earlier communication, I assume an energy distribution function of the form illustration where EkQ is a characteristic kinetic energy of the order of 1 eV in the case of H+ from H2 by electron impact. This exponential form was established in the gas phase by Hagstrum and Tate3 and Hagstrum4; the form is still valid, even though Ek0 is altered for H+ from H2 in the solid phase5. (After publication of the earlier communication concerning the H+(H2O)n family, this functional form of N(Ek) was shown to be experimentally valid for H+ fragments from H2O (ref. 6) and, as assumed earlier, Ek0 is considerably less than 1 eV (typically 0.2 eV). Open image in new window