Thermodynamic Stabilities of Linear and Crinkled Tapes and Cyclic Rosettes in Melamine−Cyanurate Assemblies:  A Model Description (2001)

In this paper we describe model calculations for the self-assembly of N,N-disubstituted melamines 1 and N-substituted cyanuric acid or 5,5-disubstituted barbituric acid derivatives 2 into linear or crinkled tapes and cyclic rosettes via cooperative hydrogen bond formation. The model description considers all possible stereoisomeric tape structures consisting of two to eight different components (270 different species in total) and one cyclic hexameric rosette structure. Furthermore, eight steric parameters (R(12)-R(28)) are included that represent the different types of steric interactions within the assemblies. Most importantly, the model calculations clearly show that the tape/rosette ratio is very sensitive to changes in parameters that directly affect the internal energy of the rosette structure. In this respect, three parameters have been characterized, i.e., the basic equilibrium constant K(0) for the bimolecular association of a melamine and cyanurate, the equilibrium constant K(r)/K(0) for the cyclization of a linear hexamer, and the parameter R(12)-a(Z)b, representing attractive or repulsive interactions between adjacent melamine and cyanurate moieties. For example, an increase in K(0) from 100 to 10,000 M(-1) ([A](0) = [B](0) = 10 mM, K(r) = 0.01 M) or in K(r) from 0.001 to 0.1 M ([A](0) = [B](0) = 10 mM, K(0) = 1000 M(-1)) raises the concentration of the rosette from <5 to approximately 90% or from approximately 10 to approximately 85%, respectively. Similarly, a change in R(12)-a(Z)b from 1.0 (no repulsive or attractive interactions) to 1.5 (slight attractive interaction) raises the rosette fraction of the mixture from 25% to 45%. In sharp contrast to this, the model calculations show that parameters that only affect the internal energy of the tapes (R(13)--R(28)) hardly change the tape/rosette ratio. For example, by changing R(13)-a(EE)a from 1.0 (no repulsive or attractive interactions) to 0.001 (maximum repulsion), the rosette fraction in the mixture changes by no more than 8%. Including all possible sterics that occur only in tapes (i.e., R(13)--R(28)), the maximum change in rosette fraction is no more than 16%. These predictions can be rationalized by considering that any change in the stability of the tapes only affects the rosette concentration by means of shifting the equilibrium between free 1 and 2 and the rosette. Since there are 270 different tapelike structures in equilibrium, this mixture represents the best buffer solution in the world. These model calculations seem to conflict with the concept of peripheral crowding as put forward by Whitesides et al., which states that bulky substituents on the periphery of the melamine (and cyanurate) components can be used to shift the tape/rosette equilibrium completely toward the rosette structure. Computer simulations (CHARMm 24.0) show that linear tapes with bulky substituents are severely distorted from planarity, while the corresponding rosette remains planar. Therefore, tapelike structures with bulky substituents are expected to have a much higher solubility than the corresponding rosettes, which can explain the observed crystal data.