Estimating the Entropic Cost of Self-Assembly of Multiparticle Hydrogen-Bonded Aggregates Based on the Cyanuric Acid·Melamine Lattice

The entropic component of the free energy of assembly for multiparticle hydrogen-bonded aggregates is analyzed using a model based on balls connected by rigid rods or flexible strings. The entropy of assembly, ΔS, is partitioned into translational, rotational, vibrational, and conformational components. While previously reported theoretical treatments of rotational and vibrational entropies for assembly are adequate, treatments of translational entropy in solution and of conformational entropyoften the two largest components of ΔSare not. This paper provides improved estimates and illustrates the methods used to obtain them. First, a model is described for translational entropy of molecules in solution (ΔStrans(sol)); this model provides physically intuitive corrections for values of ΔStrans(sol) that are based on the Sackur−Tetrode equation. This model is combined with one for rotational entropy to estimate the difference in entropy of assembly between a 4-particle aggregate and a 6-particle one. Second, an approximate analysis of a model based on balls connected by rods or strings gives an approximate estimate of the maximum contribution of conformational entropy to the difference in free energy of assembly of flexible and of rigid molecular assemblies. This analysis, although approximate, is easily applied by all types of chemists and biochemists; it serves as a guide to the design of stable molecular aggregates, and the qualitative arguments apply generally to any form of self-assembly.