{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,30]],"date-time":"2026-08-30T18:52:16Z","timestamp":1788115936300,"version":"build-2803163510"},"reference-count":70,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,15]],"date-time":"2023-10-15T00:00:00Z","timestamp":1697328000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Gels"],"abstract":"<jats:p>Structure and reversibility of cross-link junctions play pivotal roles in determining the nature of thermoreversible gelation and dynamic mechanical properties of the produced polymer networks. We attempt to theoretically explore new types of sol\u2013gel transitions with mechanical sharpness by allowing cross-links to grow without upper bound. We consider thermoreversible gelation of the primary molecules R{Af} carrying the number f of low molecular weight functional groups (gelators) A. Gelators A are assumed to form supramolecular assemblies. Some examples are: telechelic polymers (f=2) carrying \u03c0\u2013\u03c0 stacking benzene derivatives at their both ends, and trifunctional star molecules (f=3) bearing multiple hydrogen-bonding gelators. The sol\u2013gel transition of the primary molecules becomes sharper with the cooperativity parameter of the stepwise linear growth of the cross-links. There is a polymerization transition (crossover without singularity) of the junctions in the postgel region after the gel point is passed. If the gelator A tends to form supramolecular rings competitively with linear chains, there is another phase transition in the deep postgel region where the average molecular weight of the rings becomes infinite (Bose\u2013Einstein condensation of rings). As a typical example of binary cross-links where gelators A and B form mixed junctions, we specifically consider metal-coordinated binding of ligands A by metal ions B. Two types of multi-nuclear supramolecular complexes are studied: (i) linear stacking (ladder) of the sandwich A2B units, and (ii) linear train of egg-box A4B units. To find the strategy towards experimental realization of supramolecular cross-links, the average molecular weight, the gel fraction, the average length of the cross-link junctions are numerically calculated for all of these models as functions of the functionality f, the concentration of the solute molecules, and the temperature. Potential candidates for the realization of these new types of thermoreversible gelation are discussed.<\/jats:p>","DOI":"10.3390\/gels9100820","type":"journal-article","created":{"date-parts":[[2023,10,15]],"date-time":"2023-10-15T10:47:32Z","timestamp":1697366852000},"page":"820","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Thermoreversible Gelation with Supramolecularly Polymerized Cross-Link Junctions"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5852-1202","authenticated-orcid":false,"given":"Fumihiko","family":"Tanaka","sequence":"first","affiliation":[{"name":"Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Katsura, Kyoto 615-8510, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,15]]},"reference":[{"key":"ref_1","unstructured":"Guenet, J.M. (1992). 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