The width and asymmetry of the line shape of the optical transition of a sample of two dimensional (2D) molecular J-aggregates was found to be related to a finite-size effect. The 2D aggregates were domains of the ordered monolayer of the fluorescent dye molecule 3,4,9,10-perylenetetracarboxylic acid dianhydride on a KCl(100) surface. Fluorescence and fluorescence excitation (FLE) spectra were measured as a function of temperature. The system shows a pronounced superradiant emission which yields additional information on the number of coherently coupled molecules participating in the emission. From calculations of the spectra within the tight binding model we find that the finite size of the 2D ordered domains of about N = 7 × 7 molecules, in combination with a Poissonian domain-size distribution, explains the line profile. Line broadening mechanisms due to site disorder or thermal effects – although not excludable straightaway – are not needed to explain the observed FLE line profile. This yields insight into the important, but so far not well understood, relation between the line profile and the size of ordered molecular aggregates.

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