Reversible Stepwise Condensation Polymerization with Cyclization: Strictly Alternating Co-polymerization and Homopolymerization Based upon Two Orthogonal Reactions

Abstract

In a preceding work [10.1021/acs.macromol.1c00718Macromolecules2021], we have introduced a simple recursive scheme that allows us to treat stepwise linear reversible polymerizations of any kind with cyclization. This approach is used to discuss the polymerization of linear Gaussian strands (LGS) with two different reactive groups A and B on either chain end that participate in two orthogonal reactions and the strictly alternating copolymerization of LGS that carry A reactive groups with LGS equipped with type B reactive groups. The former of these cases has not been discussed theoretically in literature, the latter only regarding some special cases. We provide either analytical expressions or exact numerical solutions for the general cases with and without cyclization. Weight distributions, averages, polydispersity, and the weight fractions of cyclic and linear species are computed. All numerical solutions were tested by Monte-Carlo simulations.

Reversible Networks made of Star Polymers: Mean Field Treatment with Consideration of Finite Loops

“…These simplifications allow for an easier access to a theoretical modeling and probably a better understanding of reversible networks. Recent experiments [7][8][9][10][11][12][13][14] follow the same idea, leading sometimes to quite unexpected results. We hope that our work can contribute in explaining these observations.…”

Reversible Networks made of Star Polymers: Mean Field Treatment with Consideration of Finite Loops

“…Furthermore, we could show that this approach can be extended to consider loops involving two generations of stars polymers. Our approach builds on top of a set of balance equations that were previously used to describe reversible linear polymerization with the formation of loops of any size [40,41]. This approach provides numerically exact solutions as we have tested with a set of appropriate Monte-Carlo simulations that model loop formation in a reversible network only up to a particular generation g. Furthermore, it can be extended to time-dependent problems, to solvents of different quality including good solvents as described earlier [40], and there is the possibility to expand it with a Flory-Huggins like treatment of the interactions with poor solvents.…”

“…Furthermore, theoretical modeling up to at least generation g = 2 is necessary to understand differences between homo-polymer and AB type co-polymer systems, where reactions occur only between A and B type stars in a heterocomplementary fashion [38,39]. We want to close this gap by extending an approach for linear polymerization [40,41] towards branched systems and by analyzing the impact of finite loops up to g = 2 for a small number of arms per star, f . Furthermore, we contribute mean-field simulation data on model systems where loop formation is truncated at a particular generation g to check the quality of estimates that are based upon considering only finite g.…”

Simple and General Approach for Reversible Condensation Polymerization with Cyclization

“…7,39 We will close some of these gaps in a subsequent work where we provide a full discussion of case 3 and variant (b) of case 2. 40 Typical examples for case 1 are polymers that couple through their OH groups like dimethylsilanediol 23 or that contain self-complementary binding sites like ureidopyrimidone dimers or guanidiniocarbonyl pyrrole carboxylate zwitterions or alike. 41−45 Classical examples for variant a of case 2 include the polymerization of some hydroxy acids like ω-hydroxyundecanoic acid 23,46 or poly(4-hydroxybenzoate).…”

“…In addition to these limitations, the missing quantitative predictions for conversion or the weight fraction of rings make it quite difficult to make accurate predictions of sample average quantities like average molar mass or polydispersity. This is of quite some relevance, since it is expected that a small weight fraction of rings at high concentrations can still cause a large polydispersity of the sample. , We will close some of these gaps in a subsequent work where we provide a full discussion of case 3 and variant (b) of case 2 …”