Aggregates of proteins containing polyglutamine (polyQ) repeats are strongly associated with several neuro-degenerative diseases. The length of the repeats correlates with the severity of the disease. Previous studies have shown that pure polyQ peptides aggregate by nucleated growth polymerization and that the size of the critical nucleus (n*) decreases from tetrameric to dimeric and monomeric as length increases from Q(18) to Q(26). Why the critical nucleus size changes with repeat-length has been unclear. Using the associative memory, water-mediated, structure and energy model, we construct the aggregation free energy landscapes for polyQpeptides of different repeat-lengths. These studies show that the monomer of the shorter repeat-length (Q(20)) prefers an extended conformation and that its aggregation indeed has a trimeric nucleus (n* 3), while a longer repeat-length monomer (Q(30)) prefers a beta-hairpin conformation which then aggregates in a downhill fashion at 0.1 mM. For an intermediate length peptide (Q(26)), there is an equal preference for hairpin and extended forms in the monomer which leads to a mixed inhomogeneous nucleation mechanism for fibrils. The predicted changes of monomeric structure and nucleation mechanism are confirmed by studying the aggregation free energy profile for a polyglutamine repeat with site-specific PG mutations that favor the hairpin form, giving results in harmony with experiments on this system.