This paper presents a theoretical study on the physical interaction between polycyclic aromatic hydrocarbons (PAHs) and their clusters of different sizes in premixed laminar flames. Two models are employed for this study: a detailed PAH growth model, referred to as the kinetic Monte Carlo---aromatic site (KMC-ARS) model [Raj et al., Combust. Flame, 2009]; and a multivariate PAH population balance model, named as the PAH-primary particle (PAH-PP) model. Both the models are solved by kinetic Monte Carlo methods. PAH mass spectra are generated using the PAH-PP model, and compared to the experimentally observed spectra for a premixed laminar ethylene flame. The position of the maxima of PAH dimers in the spectra and their concentrations are found to depend strongly on the collision efficiency of PAHs. The variation in the collision efficiency with various flame and PAH parameters is studied to determine the factors on which it may depend. A correlation for the collision efficiency is proposed by comparing the computed and the observed spectra for an ethylene flame. With this correlation, a good agreement between the computed and the observed spectra for a number of premixed laminar ethylene flames is found.