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note
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The limit where the cooperativity becomes infinite formally corresponds to the limit of infinite coupling constant in an Ising chain. Hence, in this limit the helical transition becomes a true phase transition, but only for infinitely long aggregates (ref 30).
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35
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0013412622
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note
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Obviously, the energies of the first and last bonds of the aggregates can also be varied in a continuous way, rather than assigning discrete values to them. However, to avoid generating additional parameters in our model, we chose to fix the energies of the end bonds to either infinity or the appropriate energy of a helical or nonhelical bond.
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Strictly speaking, the average helicity should contain a summation over the (N - 1) bonds, rather than over the N molecules. However, this would require us to adjust the definition of pi; in this context, and in practice the effect of this improvement is negligible.
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41
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0013405261
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note
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The chemical name of the discotic molecule is N,N′,N″ -tris-{3[3′-(3,4,5-tris{(2S)-2-(2-{2-[2-(2-methoxyethoxy)-ethoxyl-ethoxy} -ethoxy)-propyloxy})-benzoylamino]-2,2′-bipyridyl}-benzene-1,3, 5-tricarbonamide.
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42
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0013444243
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note
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w - 1 with the equilibrium state at low temperature, rather than the state where the fractions of small, nonhelical oligomers approach zero.
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44
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0013457323
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note
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-1.
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46
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0035933393
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