Theory of Polymer and Soft Matter Group, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
J Chem Phys. 2012 Aug 14;137(6):064906. doi: 10.1063/1.4742192.
As a first step to understand the role of molecular or chemical polydispersity in self-assembly, we put forward a coarse-grained model that describes the spontaneous formation of quasi-linear polymers in solutions containing two self-assembling species. Our theoretical framework is based on a two-component self-assembled Ising model in which the chemical bidispersity, i.e., the presence of two distinct chemical entities, is parameterized in terms of the strengths of the binding free energies that depend on the monomer species involved in the pairing interaction. Depending upon the relative values of the binding free energies involved, different morphologies of assemblies that include both components are formed, exhibiting random, blocky or alternating ordering of the two components in the assemblies. Analyzing the model for the case of blocky ordering, which is of most practical interest, we find that the transition from conditions of minimal assembly to those characterized by strong polymerization can be described by a critical concentration that depends on the concentration ratio of the two species. Interestingly, the distribution of monomers in the assemblies is different from that in the original distribution, i.e., the ratio of the concentrations of the two components put into the system. The monomers with a smaller binding free energy are more abundant in short assemblies and monomers with a larger binding affinity are more abundant in longer assemblies. Under certain conditions the two components congregate into separate supramolecular polymeric species and in that sense phase separate. We find strong deviations from the expected growth law for supramolecular polymers even for modest amounts of a second component, provided it is chemically sufficiently distinct from the main one.
为了理解分子或化学多分散性在自组装中的作用，我们首先提出了一个粗粒化模型，用于描述在含有两种自组装物质的溶液中准线性聚合物的自发形成。我们的理论框架基于一个两组件自组装的伊辛模型，其中化学多分散性（即两种不同化学实体的存在）用依赖于参与配对相互作用的单体种类的结合自由能强度来参数化。根据涉及的结合自由能的相对值，可以形成包括两种成分的不同组装体形态，表现出两种成分在组装体中的随机、块状或交替有序。对最实际感兴趣的块状有序的情况分析模型，我们发现从最小组装条件到具有强聚合作用的条件的转变可以用依赖于两种物质浓度比的临界浓度来描述。有趣的是，组装体中单体的分布与原始分布不同，即两种成分的浓度比。具有较小结合自由能的单体在短组装体中更丰富，而具有较大结合亲和力的单体在较长组装体中更丰富。在某些条件下，两种成分会聚集到单独的超分子聚合物物种中，从而在某种意义上发生相分离。我们发现即使对于第二组分的数量适中，也会对超分子聚合物的预期生长规律产生强烈偏离，只要它在化学上与主要组分足够不同。
