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As a first step to understanding the role of molecular or chemicalpolydispersity in self-assembly, we put forward a coarse-grained model thatdescribes the spontaneous formation of quasi-linear polymers in solutionscontaining two self-assembling species. Our theoretical framework is based on atwo-component self-assembled Ising model in which the bidispersity isparameterized in terms of the strengths of the binding free energies thatdepend on the monomer species involved in the pairing interaction. Dependingupon the relative values of the binding free energies involved, differentmorphologies of assemblies that include both components are formed, exhibitingparamagnetic-, ferromagnetic- or anti ferromagnetic-like order,i.e., random,blocky or alternating ordering of the two components in the assemblies.Analyzing the model for the case of ferromagnetic ordering, which is of mostpractical interest, we find that the transition from conditions of minimalassembly to those characterized by strong polymerization can be described by acritical concentration that depends on the concentration ratio of the twospecies. Interestingly, the distribution of monomers in the assemblies isdifferent from that in the original distribution, i.e., the ratio of theconcentrations of the two components put into the system. The monomers with asmaller binding free energy are more abundant in short assemblies and monomerswith a larger binding affinity are more abundant in longer assemblies. Undercertain conditions the two components congregate into separate supramolecularpolymeric species and in that sense phase separate. We find strong deviationsfrom the expected growth law for supramolecular polymers even for modestamounts of a second component, provided it is chemically sufficiently distinctfrom the main one.

Random, blocky and alternating ordering in supramolecular polymers of chemically bidisperse monomers