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The formation mechanism of the DP network is systematically investigated. In the mean-field limit, the transition in the A-g-B CSBCP melts between the DP network and its spherical counterpart, the metastable body-centered cubic (BCC) spheres, can be either continuous or discontinuous, distinct from the typical order\u2013order transitions (OOTs) observed in conventional block copolymer melts. We further determine the critical point at which the discontinuity vanishes. Our results demonstrate that the stability of the DP phase and the continuous OOT primarily originate from the unique chain architecture of the A-g-B CSBCP.<\/jats:p>","DOI":"10.1063\/5.0357535","type":"journal-article","created":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T14:23:09Z","timestamp":1791901389000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Continuous and discontinuous transitions between double primitive network and body-centered cubic spheres"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-9522-4678","authenticated-orcid":false,"given":"Juntong","family":"He","sequence":"first","affiliation":[{"name":"School of Emergent Soft Matter, South China Advanced Institute for Soft Matter Science and Technology, South China University of Technology 1 , Guangzhou 510640,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xue-Hui","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Emergent Soft Matter, South China Advanced Institute for Soft Matter Science and Technology, South China University of Technology 1 , Guangzhou 510640,","place":["China"]},{"name":"Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology 2 , Guangzhou 510640,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2258-6757","authenticated-orcid":false,"given":"Jiajia","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Emergent Soft Matter, South China Advanced Institute for Soft Matter Science and Technology, South China University of Technology 1 , Guangzhou 510640,","place":["China"]},{"name":"Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology 2 , Guangzhou 510640,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1379-7162","authenticated-orcid":false,"given":"An-Chang","family":"Shi","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, McMaster University 3 , Hamilton, Ontario L8S 4M1,","place":["Canada"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,13]]},"reference":[{"key":"2026101310212341600_c1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1021\/acs.macromol.6b02355","volume":"50","year":"2017","journal-title":"Macromolecules"},{"issue":"2","key":"2026101310212341600_c2","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1063\/1.882522","volume":"52","year":"1999","journal-title":"Phys. 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