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Taking into account the full Coulomb potential and the excluded volume interactions, properties of dendrimers with generations g = 5, 6 with charged terminal groups and counterions in an athermal solvent are examined by lattice Monte Carlo simulations. The study treats counterions explicitly and focuses on the local structure of the systems inspected by pair correlation functions g_{ab} that provide information on distributions of monomers, terminal groups and ions in space at various temperatures T*. Special emphasis is placed on counterions and their role they play in causing conformational changes of the molecules. The simulations show that counterions penetrate the interior of the dendrimers, and there is a major increase in their concentration there as T* decreases. Some of them condense onto the terminal groups and a reduction in the mean effective charge ⟨Q⟩ of the dendrimers appears. Within the range of temperatures where the condensation (as a function of T*) is sharp the molecules weakly swell up when compared to their size at the other temperatures. This kind of behaviour is also reflected by the distributions of monomers and terminal groups.
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