Gelation in polystyrene, poly(methylphenylsilane), and poly(di-$n$-hexylsilane) induced by irradiation with $30–200\mathrm{keV}$ Ga, Si, and Au ion beams is examined and compared with that induced by MeV-order ion beams of similar linear energy transfer. The apparent $G$ values of crosslinking (crosslinks per $100\mathrm{eV}$ absorbed dose) are calculated using the Charlesby-Pinner relationship, and shown to be dramatically lower than for the corresponding MeV ion beams. This decrease is attributed due to the reduced ion track radius and an increase in the density of crosslinking points. The apparent crosslinking $G$ value obtained by the Charlesby-Pinner relationship represents only the crosslinking points contributing to gelation, and other points such as intramolecular crosslinking in the core of the ion track are not counted in the relationship. The total volume of ion tracks is considered to be the most important feature determining the gel fraction produced by the ion beams. A new formulation that provides a good explanation of the gelation of the polymer is proposed, with applicability to ion beams with energy of keV to MeV order.

• Received 11 May 2004

DOI:https://doi.org/10.1103/PhysRevB.70.144203