ESTIMATING THE ENTROPIC COST OF SELF-ASSEMBLY OF MULTIPARTICLE HYDROGEN-BONDED AGGREGATES BASED ON THE CYANURIC ACID-CENTER-DOT-MELAMINE LATTICE

The entropic component of the free energy of assembly for multiparticl e hydrogen-bonded aggregates is analyzed using a model based on balls connected by rigid rods or flexible strings. The entropy of assembly, Delta S, is partitioned into translational, rotational, vibrational, a nd conformational components. While previously reported theoretical tr eatments of rotational and vibrational entropies for assembly are adeq uate, treatments of translational entropy in solution and of conformat ional entropy-often the two largest components of Delta S-are not, Thi s paper provides improved estimates and illustrates the methods used t o obtain them. First, a model is described for translational entropy o f molecules in solution (Delta S-trans(sol)); this model provides phys ically intuitive corrections for values of hS(trans)(sol) that are bas ed 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 g-particle one. Second, an approx imate analysis of a model based on balls connected by rods or strings gives an approximate estimate of the maximum contribution of conformat ional entropy to the difference in free energy of assembly of flexible and of rigid molecular assemblies. This analysis, although approximat e, is easily applied by all types of chemists and biochemists; it serv es as a guide to the design of stable molecular aggregates, and the qu alitative arguments apply generally to any form of self-assembly.