Amplification of chirality in helical supramolecular polymers: the majority-rules principle

Amplification of chirality, being a strongly nonlinear response of the optical activity of helical polymers to a small (net) amount of optically active material, has recently been discovered in supramolecular copolymers. Apart from the sergeants-and-soldiers type we discussed in earlier work, chirality amplification can also occur in copolymers consisting of the two enantiomeric forms of the monomeric building blocks. We outline the first theoretical treatment of this "majority-rules" type of chirality amplification in self-assembled aggregates. Our treatment, which is based on the one-dimensional, two-component Ising model, is analytical and exact in the infinite-chain limit. We find a strong dependence of the strength of the chirality amplification on the free-energy penalty of a helix reversal as well as on that of a mismatch between the preferred helical handedness of a monomer and the actual screw sense of the bond that follows it. The strength of the chirality amplification shows a monotonic increase with increasing helix reversal penalty but a strongly nonlinear and nonmonotonic dependence on the mismatch penalty

Impact of steric interactions on the helical transition in assemblies of discotic molecules

We investigate theoretically the effect of excluded-volume interactions on the helical configurational transition of supramolecular assemblies in solutions of chiral disklike molecules. To this end, we set up a second-virial theory within the context of the helical self-assembly of rodlike objects. We find that interaggregate interactions shift both the helical-transition point and the sharpness of the transition. For realistic values of the model parameters, the helical-transition temperature shifts by several degrees, and the more so the higher the concentration of assembling material. The mean aggregation number is also affected by the interactions, albeit only by a modest amount, unless the solution becomes very concentrated

Amplification of chirality in helical supramolecular polymers

We theoretically studied the sergeants-and-soldiers principle of chirality amplification in self-assembled, supramolecular helical polymers and show that a mapping is possible on a two-component Ising chain, in which one of the components has a spin of fixed orientation. The relative abundance of this component is regulated by a chemical potential. Our theory quantitatively describes recently published measurements of the optical activity of linear assemblies of certain discotic molecules in solution. We find that the strength of the chirality amplification depends strongly on the strength of the coupling between the spins, which translates into a free-energy penalty put on a helix reversal along the backbone of the self-assembled polymer

Amplification of chirality in helical supramolecular polymers

We theoretically studied the sergeants-and-soldiers principle of chirality amplification in self-assembled, supramolecular helical polymers and show that a mapping is possible on a two-component Ising chain, in which one of the components has a spin of fixed orientation. The relative abundance of this component is regulated by a chemical potential. Our theory quantitatively describes recently published measurements of the optical activity of linear assemblies of certain discotic molecules in solution. We find that the strength of the chirality amplification depends strongly on the strength of the coupling between the spins, which translates into a free-energy penalty put on a helix reversal along the backbone of the self-assembled polymer

Role of end effects in helical aggregation

End effects are known to play a pivotal role in equilibrium polymerization. To investigate their role in detail, we apply constraints to the first and last bonds of model linear aggregates that exhibit a helix-coil type configurational transition. Three different classes of behavior manifest themselves. These can be distinguished by the presence or absence of re-entrance behavior of nonhelical conformations at constant helical-bond strength, as well as by the dependence of the locations of the polymerization and helical transitions on the cooperativity of the helical transition. A comparison of the theory with experimental data on solutions of chiral discotic molecules in n-butanol shows that only one of the three classes can account for the experimental observations

Helical transition of polymer-like assemblies in solution

A minimal model is presented for helix-coil type transitions in solutions of self-assembled supramolecular polymers. The diagram of states calculated using this model shows that there are essentially two ordering regimes, one where the polymerization transition and the helical transition coincide and one where they are separate. In both regimes a strong coupling exists between the growth and the helical transition of the supramolecular polymers. Comparison of the theory with experimental data confirms that the minimal model provides an adequate description of helix-coil type transitions in self-assembled polymers and that these transitions can be highly cooperative

Amplification of chirality in benzene tricarboxamide helical supramolecular polymers

The chirality of benzene tricarboxamides is expressed and amplified into the helicity of self-assembled columnar aggregates according to sergeants and soldiers' and majority rules' principles; the strength of the amplification is analyzed quant. and the effect of the no. of chiral groups in the sergeants is studied