MacromoleculesPub Date : 2025-09-15DOI: 10.1021/acs.macromol.5c01483
Yiheng Wu, , , Artem M. Rumyantsev*, , and , Juan J. de Pablo*,
{"title":"Manifold of Polyampholyte Necklaces: From Charge Migration to Hierarchical Structure","authors":"Yiheng Wu, , , Artem M. Rumyantsev*, , and , Juan J. de Pablo*, ","doi":"10.1021/acs.macromol.5c01483","DOIUrl":"10.1021/acs.macromol.5c01483","url":null,"abstract":"<p >Single-chain conformations of charge-imbalanced polyampholytes are controlled by an interplay of nonelectrostatic interactions between monomers, defined by the solvent quality, and Coulomb forces between charged monomers, which are sensitive to their primary sequence. Electrostatic interactions manifest themselves as effective short-range attractions between opposite charges and, simultaneously, as long-range repulsions owing to a net global charge of the chain. As a result, polyampholytes can adopt globular, stretched, or intermediate necklace conformations. To provide a complete description of their conformational behavior, we consider chains with Markov charge statistics and construct a scaling diagram of states in the coordinates of charge blockiness and solvent quality. Ten scaling regimes of various necklaces are identified, which can be classified into three types: (i) “charge-in-beads” necklaces form at moderate charge blockiness, with the bead size defined by the Rayleigh instability criterion; (ii) “charge-in-strings” necklaces are stable at higher blockiness of like charges, which enables the net charge imbalance to migrate from the beads to the strings; (iii) “hierarchical” necklaces, which are necklace-in-necklace conformations identified herein for the first time, comprise beads of two different sizes that coexist when the charge blockiness is high and the solvent quality is poor. For all three types of necklaces, scaling predictions are quantitatively confirmed by molecular dynamics simulations. Our findings on the conformational statistics of charge-imbalanced polyampholytes may contribute to improved prediction and classification of the structure of intrinsically disordered proteins/regions (IDPs/IDRs).</p>","PeriodicalId":51,"journal":{"name":"Macromolecules","volume":"58 18","pages":"9832–9850"},"PeriodicalIF":5.2,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://pubs.acs.org/doi/pdf/10.1021/acs.macromol.5c01483","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MacromoleculesPub Date : 2025-09-14DOI: 10.1021/acs.macromol.5c01830
Anne N. Radzanowski, , , Hoda Shokrollahzadeh Behbahani, , , William McCambridge, , , Clay Gensel, , , Catherine Spence, , , Karen I. Winey*, , and , E. Bryan Coughlin*,
{"title":"Polyhalohydrins: Investigating Vicinal Functionalities by Ring-Opening of Epoxides on Polyolefins","authors":"Anne N. Radzanowski, , , Hoda Shokrollahzadeh Behbahani, , , William McCambridge, , , Clay Gensel, , , Catherine Spence, , , Karen I. Winey*, , and , E. Bryan Coughlin*, ","doi":"10.1021/acs.macromol.5c01830","DOIUrl":"10.1021/acs.macromol.5c01830","url":null,"abstract":"<p >Halohydrins are functional groups that are underexplored in polymer science. This study synthesized and examined structure–property relationships of halohydrin-functionalized polymers derived from polycyclooctene (PCOE), which was obtained via ring-opening metathesis polymerization (ROMP). The polyhalohydrins, including polychlorohydrin, polybromohydrin, and polyiodohydrin, were produced through a two-step process involving epoxidation of PCOE followed by epoxide ring-opening using hydrochloric, hydrobromic, or hydroiodic acid. These stereoirregular and regioirregular polymers are amorphous as measured by differential scanning calorimetry and X-ray scattering. Lap joint shear testing revealed an enhanced adhesive performance in polychlorohydrin and polybromohydrin, with the former demonstrating nearly three times the ultimate shear stress compared to a model polyethylene, hydrogenated PCOE. Additionally, contact angle measurements and surface free energy analysis showed an increase in hydrophilicity and polarity from iodine- to bromine- to chlorine-functionalized polyhalohydrins, aligning with trends in adhesion strength. These results underscore the potential of halohydrin functionalization as a versatile approach for tuning surface properties, offering new opportunities for polymer-to-polymer transformations.</p>","PeriodicalId":51,"journal":{"name":"Macromolecules","volume":"58 18","pages":"10073–10083"},"PeriodicalIF":5.2,"publicationDate":"2025-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Steric and Electronic Effects Manipulate Cyanoguanidine Urea Networks to Achieve Ultrastrength, Toughness, and Malleability: Structural Design, Synthesis, and Performances","authors":"Yanlin Liu, , , Zhen Yu*, , , Yajin Fang, , , Jinping Ni, , , Junping Zhang*, , and , Zhaobin Tang*, ","doi":"10.1021/acs.macromol.5c01829","DOIUrl":"10.1021/acs.macromol.5c01829","url":null,"abstract":"<p >Although the development of covalent adaptive networks has opened up the possibility of recycling thermosets, the relentless pursuit of such materials must still reconcile the contradiction between comprehensive performance, particularly the contradiction between ultrahigh mechanical strength and malleability or recyclability. To address this issue, a molecular design strategy utilizing synergistic steric and electronic effects in the cyanoguanidine urea (CGUA) network was developed in this work. The dipole–dipole interaction enhances the cohesive energy density and mechanical enhancement, whereas tailored steric hindrance modulates the dynamic bond activation barrier. This yields CGUA networks exhibiting unprecedented mechanical properties, including as tensile strength of up to 150.6 MPa, modulus exceeding 1821 MPa, and toughness surpassing 2996 J m<sup>–2</sup>, while retaining malleability at 160 and 180 °C. By varying the steric and electronic properties of substituents within the guanidine urea structure, tunable control over polymerization, network dynamics, and mechanical properties can be achieved. This work provides a novel strategy to decouple mechanical robustness from dynamic functionality in recyclable polymers.</p>","PeriodicalId":51,"journal":{"name":"Macromolecules","volume":"58 18","pages":"9645–9652"},"PeriodicalIF":5.2,"publicationDate":"2025-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Synthesis of ABC-Type Periodic Terpolymers through a Reversible Lock–Unlock Mechanism in Living Carbanionic Polymerization","authors":"Hong Yan, , , Feiyang Yu, , , Siwei Chen, , , Haitao Leng, , , Xuefei Wang, , , Li Han, , , Hongyuan Bai*, , and , Hongwei Ma*, ","doi":"10.1021/acs.macromol.5c01374","DOIUrl":"10.1021/acs.macromol.5c01374","url":null,"abstract":"<p >Precise sequence control in polymer synthesis remains a paramount challenge in contemporary macromolecular engineering and requires the development of innovative methodologies. Herein, we report a reversible “Lock–Unlock” mechanism in living carbanionic polymerization, achieved through the ingenious design of the surrounding structure of carbanions, enabling the synthesis of ABC-type periodic terpolymers. Nuclear magnetic resonance (NMR) spectroscopy and density functional theory (DFT) simulations demonstrate that the bridged-ring steric hindrance in 5-methylene-10,11-dihydro-5H-dibenzo[a,d][7]annulene (MDDAE) induced the formation of a half-enclosed carbanion structure in MDDAE-Li. Notably, MDDAE-Li exhibits unique monomer-selective copolymerization characteristics, undergoing nucleophilic reactions with 1-phenyl-1,3-butadiene (1-PB) but not with styrene (St). Therefore, 1-PB acts as a molecular “key” unlocking MDDAE/St copolymerization. Leveraging this monomer-selective behavior of MDDAE-Li, we established a reversible “Lock–Unlock” ternary copolymerization system (MDDAE/1-PB/St) that achieves precise ABC-type periodic terpolymers. Reversibility of the “Lock–Unlock” switch is governed by 1-PB consumption during ternary copolymerization (MDDAE/1-PB/St)-polymerization halts at 1-PB depletion and resumes upon its reintroduction. These significant findings not only enhance the mechanistic understanding of living anionic polymerization but also establish a theoretical framework for synthesizing sequence-defined copolymers.</p>","PeriodicalId":51,"journal":{"name":"Macromolecules","volume":"58 18","pages":"9918–9929"},"PeriodicalIF":5.2,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Recyclable Biomass-Derived Polyethylene-like Plastics","authors":"Zhihao Wang, , , En Fang, , , Liangyu Chen, , , Yuhao Guo, , , Zhiqiang Fan, , and , Shaofei Song*, ","doi":"10.1021/acs.macromol.5c01976","DOIUrl":"10.1021/acs.macromol.5c01976","url":null,"abstract":"<p >Recyclability and reusability of polymeric materials to reduce plastic wastes and alleviate environmental burdens have received extensive attention. Cyclic olefins with low ring strain and their depolymerizable polymers are very promising candidates. Introducing a linear alkyl side chain with a strong crystallization tendency to the backbone can endow the developed cyclopentene-based polypentenamers with comparable tensile properties to polyethylene. Nevertheless, the emerging challenge is their potentially high manufacturing cost and low sustainability, since stoichiometric petrochemical feedstocks need to be employed. To address the chemistry issues, we probe herein the protocol to prepare biomass-derived polypentenamers. Cyclopentene derivative methyl 3-cyclopentenecarboxylate was used to form a depolymerizable polymeric backbone and to create a powerful platform for synthesis of crystalline polypentenamers. Three biomass alcohols including biologically active natural product melissyl alcohol would act as the crystalline modules to be introduced into the polymers by transesterification using very few base catalysts. These depolymerizable plastics with a biomass content up to 83.1 wt % showed enhanced mechanical properties and could perform as mulch films to promote the growth of leafy crops. Complete depolymerization of these polymers to afford polymerizable monomers realized full closed-loop recycling. Diverse postfunctionalization to form versatile substances confirmed their reusability.</p>","PeriodicalId":51,"journal":{"name":"Macromolecules","volume":"58 18","pages":"9712–9723"},"PeriodicalIF":5.2,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MacromoleculesPub Date : 2025-09-13DOI: 10.1021/acs.macromol.5c00311
Shiyu Gu, , , Hui Liu, , , Qiaoqiao Shen, , , Haitao Wu, , , Yan Peng, , , Mi Luo, , , Bangjiao Ye, , , Hongjun Zhang*, , and , Jinrong Wu*,
{"title":"Monitoring the Stress-Activated Region in Hydrogen-Bonded Supramolecular Polymer Networks","authors":"Shiyu Gu, , , Hui Liu, , , Qiaoqiao Shen, , , Haitao Wu, , , Yan Peng, , , Mi Luo, , , Bangjiao Ye, , , Hongjun Zhang*, , and , Jinrong Wu*, ","doi":"10.1021/acs.macromol.5c00311","DOIUrl":"10.1021/acs.macromol.5c00311","url":null,"abstract":"<p >To explore the evolution of the stress-activated region in supramolecular network polymers, we incorporate aggregation-induced quenching moieties into macromolecular chains. Upon cutting the material, a significant increase in the fluorescence intensity is observed around the cut region, signaling the formation of a stress-activated region. This fluorescence enhancement is attributed to the dissociation of hydrogen bonds, which increases the free-volume fraction, as revealed by positron annihilation lifetime spectroscopy. As the cut section anneals, the fluorescence intensity, width, and free-volume fraction of the stress-activated region gradually decrease, indicating repair of the network structure. Notably, the repair process begins at the bulk side and progresses toward the cut section. The rate of this repair process can be quantified by monitoring the reduction in the region width. Furthermore, the evolution of the stress-activated region is strongly influenced by the density of hydrogen bonds, which govern molecular mobility. These findings offer valuable insights into the molecular dynamics of supramolecular interactions and guide the rational design of advanced supramolecular network polymers.</p>","PeriodicalId":51,"journal":{"name":"Macromolecules","volume":"58 18","pages":"9740–9746"},"PeriodicalIF":5.2,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MacromoleculesPub Date : 2025-09-12DOI: 10.1021/acs.macromol.5c01477
Zakarya Baouch, , , Leire Sangroniz, , , Yunxiang Shi, , , Elmar Pöselt, , , Alejandro J. Müller*, , and , Dario Cavallo*,
{"title":"Self-Nucleation Enables Polymorphic Selection in Thermoplastic Polyurethanes","authors":"Zakarya Baouch, , , Leire Sangroniz, , , Yunxiang Shi, , , Elmar Pöselt, , , Alejandro J. Müller*, , and , Dario Cavallo*, ","doi":"10.1021/acs.macromol.5c01477","DOIUrl":"10.1021/acs.macromol.5c01477","url":null,"abstract":"<p >This work investigates the self-nucleation behavior of thermoplastic polyurethanes (TPUs) with hard segment (HS) contents ranging from 29 to 80 wt %. Differential scanning calorimetry (DSC) reveals that upon cooling from the isotropic melt (<i>Domain I</i>), crystallization initially occurs as a single low-temperature exothermic peak associated with the formation of metastable <i>Form I</i>. However, when the self-nucleation temperature (<i>T</i><sub>s</sub>) is within <i>Domain II</i> (the self-nucleation <i>Domain</i>), a second, higher-temperature crystallization exotherm emerges and progressively dominates as <i>T</i><sub>s</sub> decreases, indicating a change in polymorphic crystallization to the more ordered <i>Form II</i>. Therefore, self-nucleation not only accelerates crystallization kinetics but also alters the polymorphic outcome, favoring <i>Form II</i> over <i>Form I</i>. This interpretation is further supported by ex situ Wide-Angle X-ray Diffraction (WAXD) and polarized light optical microscopy (PLOM) measurements, which confirm the increasing presence of <i>Form II</i> with decreasing <i>T</i><sub>s</sub>, as evidenced by its characteristic diffraction patterns and by the growing presence of <i>Form II</i> birefringent spherulites, particularly in high-HS-content TPUs. Notably, even TPUs with low HS content (29–33%), which are typically incapable of crystallizing in <i>Form II</i> under nonisothermal conditions, develop this polymorph induced by the thermal treatment applied by self-nucleation. The reason behind the formation of <i>Form II</i> by self-nucleation is the persistence of interurethane hydrogen bonds in the melt, which may favor the crystallization of <i>Form II</i> due to its higher content of bonded carbonyl and N–H groups with respect to <i>Form I</i>. These findings demonstrate that self-nucleation enables precise control over polymorphic selection in TPUs across a wide compositional range, offering a versatile strategy for tailoring material properties through thermal processing.</p>","PeriodicalId":51,"journal":{"name":"Macromolecules","volume":"58 18","pages":"9876–9886"},"PeriodicalIF":5.2,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://pubs.acs.org/doi/pdf/10.1021/acs.macromol.5c01477","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MacromoleculesPub Date : 2025-09-12DOI: 10.1021/acs.macromol.5c01524
Xianchuan Ran, , , Qingshu Dong*, , , Li Peng, , , Xianbo Huang*, , and , Weihua Li*,
{"title":"Program Asymmetric Binary Packing Lattices of AB1CB2 Tetrablock Terpolymers","authors":"Xianchuan Ran, , , Qingshu Dong*, , , Li Peng, , , Xianbo Huang*, , and , Weihua Li*, ","doi":"10.1021/acs.macromol.5c01524","DOIUrl":"10.1021/acs.macromol.5c01524","url":null,"abstract":"<p >ABC-type block terpolymers have great potential to self-assemble into rich ordered nanostructures, e.g., binary cylindrical structures. Recent experiments observed novel binary cylindrical structures in AB<sub>1</sub>CB<sub>2</sub> linear tetrablock terpolymers, which have a high coordination number of A cylinder (CN<sub>A</sub> = 8). To elucidate the formation mechanism of high-CN<sub>A</sub> binary cylindrical phases and thus to stabilize more high-CN<sub>A</sub> phases, we investigate the self-assembly of AB<sub>1</sub>CB<sub>2</sub> block copolymers, focusing on the exploration of distinct high-CN<sub>A</sub> cylindrical phases. We introduce a polygonal tiling approach to divide the planar space into different regions for two B blocks to fill through local separation. Based on this approach, the transition mechanism between different binary phases is clarified. Following the transition mechanism, we predict a multitude of high-CN<sub>A</sub> binary cylindrical phases by tailoring the key architectural parameters such as the volume fraction or the conformational parameter of the A block, including those with CN<sub>A</sub> = 6, 7, 8, 9, 10, and 12. Our theoretical prediction of so many novel binary cylindrical phases is expected to promote further experimental studies on the self-assembly of ABC-type block copolymers.</p>","PeriodicalId":51,"journal":{"name":"Macromolecules","volume":"58 18","pages":"9851–9861"},"PeriodicalIF":5.2,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MacromoleculesPub Date : 2025-09-12DOI: 10.1021/acs.macromol.5c01540
Chenchen Zhang, , , Jie Liang, , , Yunfei Yu, , , Yi Zhao, , , Shunan Feng, , , Wenxiong Shi*, , and , Jianqiang Meng*,
{"title":"Synergistic Rigid Twisted and Fluorinated Architectures in Zwitterionic Poly(arylene ether sulfone) for Ultrahigh Water/Salt Selectivity","authors":"Chenchen Zhang, , , Jie Liang, , , Yunfei Yu, , , Yi Zhao, , , Shunan Feng, , , Wenxiong Shi*, , and , Jianqiang Meng*, ","doi":"10.1021/acs.macromol.5c01540","DOIUrl":"10.1021/acs.macromol.5c01540","url":null,"abstract":"<p >High-performance desalination membranes require polymers with optimized free volume and selective transport properties. In this work, the effects of incorporating rigid monomers into zwitterionic poly(arylene ether sulfone) (PAES) membranes on water and salt transport behavior were investigated, grounded in solution-diffusion theory. Three rigid monomers, 9,9-di(4-hydroxyphenyl)fluorene (BHF), 1,1’-binaphthyl-2-phenol (BNP), and 3,6-dihydroxy-9-trifluoromethyl-9-phenylxanthene (3FR), were selected to modify polymer structure. The results demonstrate that the introduction of rigid monomers enhances the free volume and water uptake of the membranes. Notably, the 3FR-based membranes, incorporating both rigid twisted structures and fluorinated groups, exhibited a synergistic effect, significantly improving water diffusion while suppressing salt diffusion. The presence of fluorine atoms in 3FR created stable hydrophobic channels, which not only facilitated rapid water transport but also effectively hindered salt permeation, resulting in superior water/salt selectivity. The study reveals that the combination of rigid and fluorinated structures provides a promising strategy for designing high-performance desalination membranes.</p>","PeriodicalId":51,"journal":{"name":"Macromolecules","volume":"58 18","pages":"10110–10119"},"PeriodicalIF":5.2,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MacromoleculesPub Date : 2025-09-12DOI: 10.1021/acs.macromol.5c01519
Jiting Tian, , , Jean-Louis Barrat*, , and , Walter Kob*,
{"title":"Influence of Preparation and Architecture on the Elastic Modulus of Polymer Networks","authors":"Jiting Tian, , , Jean-Louis Barrat*, , and , Walter Kob*, ","doi":"10.1021/acs.macromol.5c01519","DOIUrl":"10.1021/acs.macromol.5c01519","url":null,"abstract":"<p >The elastic modulus <i>G</i> of a polymer network depends notably on parameters such as the initial concentration of the monomers before the synthesis (ρ<sub>0</sub>), the density of the cross-linker, or the topology of the network. Understanding how these factors influence the stiffness of the sample is hampered by the fact that, in experiments, it is difficult to tune them individually. Here, we use coarse-grained molecular dynamics simulations to study how these quantities, as well as excluded volume interactions, affect the elastic modulus of the network. We find that, for a regular diamond network, <i>G</i> is independent of the initial monomer concentration, while for disordered networks (monodisperse or polydisperse), the modulus increases with ρ<sub>0</sub>, at odds with the classical predictions for rubber elasticity. Analysis of the network structure reveals that, for the disordered networks, defects contribute only weakly to the observed increase, and that instead the ρ<sub>0</sub>-dependence of <i>G</i> can be rationalized by the presence of a prestrain in the sample. This prestrain can be quantified by the topological factor introduced in the affine network theory (ANT). Comparison of the disordered networks with their phantom counterparts reveals that weakly cross-linked systems show a stronger ρ<sub>0</sub>-dependence of <i>G</i> due to an increase in entanglements at higher ρ<sub>0</sub>, and that the polydisperse networks contain more entanglements than the monodisperse ones with the same average strand length. Finally, we discuss the quantitative application of ANT to the simulated real networks and their phantom counterparts and conclude that the presence of excluded volume effects must be comprehensively taken into account to achieve a qualitative understanding of the mechanical modulus of the disordered networks.</p>","PeriodicalId":51,"journal":{"name":"Macromolecules","volume":"58 18","pages":"10181–10191"},"PeriodicalIF":5.2,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}