  Recently developed linker-mediated vitrimers based on metathesis of
dioxaborolanes with various commercially available polymers have shown both
good processability and outstanding performance, such as mechanical, thermal,
and chemical resistance, suggesting new ways of processing cross-linked
polymers in industry, of which the design principle remains unknown [M.
Rottger, et al., Science 356, 62 (2017)]. Here we formulate a theoretical
framework to elucidate the phase behaviour of the linker-mediated vitrimers, in
which entropy plays a governing role. We find that with increasing the linker
concentration, vitrimers undergo a reentrant gel-sol transition, which explains
a recent experiment [S. Wu, H. Yang, S. Huang, Q. Chen, Macromolecules 53, 1180
(2020)]. More intriguingly, at the low temperature limit, the linker
concentration still determines the cross-linking degree of the vitrimers, which
originates from the competition between the conformational entropy of polymers
and the translational entropy of linkers. Our theoretical predictions agree
quantitatively with computer simulations, and offer guidelines in understanding
and controlling the properties of this newly developed vitrimer system.
