Analysis of the noncovalent, noncooperative self-association of identical aromatic molecules assumes that the equilibrium self-association constants are either independent of the number of molecules (the EK-model) or change progressively with increasing aggregation (the AK-model). The dependence of the self-association constant on the number of molecules in the aggregate (i.e., the profile of the equilibrium constant) was empirically derived in the AK-model but, in order to provide some physical understanding of the profile, it is proposed that the sources for attenuation of the equilibrium constant are the loss of translational and rotational degrees of freedom, the ordering of molecules in the aggregates and the electrostatic contribution (for charged units). Expressions are derived for the profiles of the equilibrium constants for both neutral and charged molecules. Although the EK-model has been widely used in the analysis of experimental data, it is shown in this work that the derived equilibrium constant, K(EK), depends on the concentration range used and hence, on the experimental method employed. The relationship has also been demonstrated between the equilibrium constant K(EK) and the real dimerization constant, K(D), which shows that the value of K(EK) is always lower than K(D).