A Simple Thermodynamic Model for Quantitatively Addressing Cooperativity in Multicomponent Self‐Assembly Processes—Part 1: Theoretical Concepts and Application to Monometallic Coordination Complexes and Bimetallic Helicates Possessing Identical Binding Sites

Abstract

A thermodynamic model has been developed for quantitatively estimating cooperativity in supramolecular polymetallic [M(m)L(n)] assemblies, as the combination of two simple indexes measuring intermetallic (I(c)MM) and interligand (I(c)LL) interactions. The usual microscopic intermolecular metal-ligand affinities (f(i)(M,L)) and intermetallic interaction parameters (uMM), adapted to the description of successive intermolecular binding of metal ions to a preorganized receptor, are completed with interligand interactions (uLL) and effective concentrations (c(eff)), accounting for the explicit free energy associated with the aggregation of the ligands forming the receptor. Application to standard monometallic pseudo-octahedral complexes [M(L)(n)(H2O)(6 - n)] (M = Co, Ni, Hf, L = ammonia, fluoride, imidazole, n = 1-6) systematically shows negative cooperativity (uLL < 1), which can be modulated by the electronic structures, charges, and sizes of the entering ligands and of the metal ions. Extension to the self-assembly of more sophisticated bimetallic helicates possessing identical binding sites is discussed, together with the origin of the positively cooperative formation of [Eu2(L3)3].

A Simple Thermodynamic Model for Quantitatively Addressing Cooperativity in Multicomponent Self‐Assembly Processes—Part 2: Extension to Multimetallic Helicates Possessing Different Binding Sites

“…[1] Application of Equation (1) for modeling the formation of standard monometallic coordination complexes successfully reproduces experimental stability constants, and it further provides a quantitative analysis of the cooperativity (i.e., deviation from repetitive statistical binding) associated with the successive binding of ligands to a single metal. [1] Related mathematical analyses of the selfassembly of bimetallic triple-stranded helicates [Eu 2 (Lk) 3 ] (k = 1-3) is complicated by the various possible combinations of metals and ligands in the final complexes, and the fitting process fails for k = 1 or 2, because of the too limited sets of available experimental stability constants. For [Eu 2 (L3) 3 ], a sufficient amount of experimental data is accessible, and the use of Equation (1) eventually demonstrates that the assembly process is driven to completion by positive cooperativity, originating from attractive interligand interactions.…”

“…He eventually concluded that statistical binding occurs, [4] in contrast with the positively cooperative process originally suggested by Lehn. [2,3] However, Ercolanis model only considers the three first terms of Equation (1), [1] and it neglects the specific intramolecular interactions described by the last two terms. Therefore, the latter approach is only adequate, when both intramolecular interactions (intermetallic + interligand) are strictly proportional to the total number of bonds (mn) connecting the m + n components in each [M m (L) n ] complex.…”

“…Keywords: cooperativity · helicate structures · lanthanides · thermodynamics Although the extended site-binding model, mathematically formulated in Equation (1), has benefited from its application to basic complexation processes for its validation, [1] it is not limited to systems that display identical binding sites. It may apply, at least theoretically, to any multicomponent assembly process, and the famous self-assembly of Lehns double-stranded trimetallic helicates [Cu 3 (Lk) 2 ] 3 + (k = 4, 5) plays a crucial role in this context, because 1) it involves (slightly) different binding sites along the strands, and 2) the associated thermodynamic constants have been originally interpreted within the frame of positive cooperativity according to Scatchard plots.…”

“…For [Eu 2 (L3) 3 ], a sufficient amount of experimental data is accessible, and the use of Equation (1) eventually demonstrates that the assembly process is driven to completion by positive cooperativity, originating from attractive interligand interactions. [1] Abstract: The extended site-binding model, which explicitly separates intramolecular interactions (i.e., intermetallic and interligand) from the successive binding of metal ions to polytopic receptors, is used for unravelling the selfassembly of trimetallic double-stranded Cu I and triple-stranded Eu III helicates. A thorough analysis of the available stability constants systematically shows that negatively cooperative processes operate, in strong contrast with previous reports invoking either statistical behaviours or positive cooperativity.…”

Metallo-supramolecular modules as a paradigm for materials science

“…The resulting complicated and aesthetically appealing structures have provided the driving force to rationalize their formation, culminating in 'the principle of maximum site occupancy' [36,37]. Here, we discuss the important aspects of macromolecular assemblies that are formed by the interaction between metal ions and ditopic ligands [38].…”