Functional Polymer Solutions and Gels Physics and Novel Applications Printed Edition of the Special Issue Published in Polymers www.mdpi.com/journal/polymers Florian J. Stadler and Bing Du Edited by Functional Polymer Solutions and Gels—Physics and Novel Applications Functional Polymer Solutions and Gels—Physics and Novel Applications Special Issue Editors Florian J. Stadler Bing Du MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin Special Issue Editors Florian J. Stadler Shenzhen University China Bing Du Shenzhen University China Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Polymers (ISSN 2073-4360) (available at: https://www.mdpi.com/journal/polymers/special issues/Polymer Solutions Gels). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year , Article Number , Page Range. ISBN 978-3-03936-230-1 ( H bk) ISBN 978-3-03936-231-8 (PDF) c © 2020 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Bing Du and Florian J. Stadler Functional Polymer Solutions and Gels—Physics and Novel Applications Reprinted from: Polymers 2020 , 12 , 676, doi:10.3390/polym12030676 . . . . . . . . . . . . . . . . . 1 Zhi-Chao Yan, Florian J. Stadler, Pierre Guillet, Cl ́ ement Mugemana, Charles-Andr ́ e Fustin, Jean-Fran ̧ cois Gohy and Christian Bailly Linear and Nonlinear Dynamic Behavior of Polymer Micellar Assemblies Connected by Metallo-Supramolecular Interactions Reprinted from: Polymers 2019 , 11 , 1532, doi:10.3390/polym11101532 . . . . . . . . . . . . . . . . 7 Zhi-Chao Yan, Chandra Sekhar Biswas and Florian J. Stadler Rheological Study on the Thermoreversible Gelation of Stereo-Controlled Poly( N -Isopropylacrylamide) in an Imidazolium Ionic Liquid Reprinted from: Polymers 2019 , 11 , 783, doi:10.3390/polym11050783 . . . . . . . . . . . . . . . . . 29 Alberto Garc ́ ıa-Pe ̃ nas, Chandra Sekhar Biswas, Weijun Liang, Yu Wang, Pianpian Yang and Florian J. Stadler Effect of Hydrophobic Interactions on Lower Critical Solution Temperature for Poly( N -isopropylacrylamide-co-dopamine Methacrylamide) Copolymers Reprinted from: Polymers 2019 , 11 , 991, doi:10.3390/polym11060991 . . . . . . . . . . . . . . . . . 47 Yi Wang Reynolds Stress Model for Viscoelastic Drag-Reducing Flow Induced by Polymer Solution Reprinted from: Polymers 2019 , 11 , 1659, doi:10.3390/polym11101659 . . . . . . . . . . . . . . . . 69 Adrianna Skwira, Adrian Szewczyk and Magdalena Prokopowicz The Effect of Polydimethylsiloxane-Ethylcellulose Coating Blends on the Surface Characterization and Drug Release of Ciprofloxacin-Loaded Mesoporous Silica Reprinted from: Polymers 2019 , 11 , 1450, doi:10.3390/polym11091450 . . . . . . . . . . . . . . . . 81 Cristina Monteser ́ ın, Miren Blanco, Nieves Murillo, Ana P ́ erez-M ́ arquez, Jon Maudes, Jorge Gayoso, Jose Manuel Laza, Est ́ ıbaliz Hern ́ aez, Est ́ ıbaliz Aranzabe and Jose Luis Vilas Novel Antibacterial and Toughened Carbon-Fibre/Epoxy Composites by the Incorporation of TiO 2 Nanoparticles Modified Electrospun Nanofibre Veils Reprinted from: Polymers 2019 , 11 , 1524, doi:10.3390/polym11091524 . . . . . . . . . . . . . . . . 97 Guoping Guan, Chenglong Yu, Meiyi Xing, Yufen Wu, Xingyou Hu, Hongjun Wang and Lu Wang Hydrogel Small-Diameter Vascular Graft Reinforced with a Braided Fiber Strut with Improved Mechanical Properties Reprinted from: Polymers 2019 , 11 , 810, doi:10.3390/polym11050810 . . . . . . . . . . . . . . . . . 111 Chris Steffi, Zhilong Shi, Chee Hoe Kong, Sue Wee Chong, Dong Wang and Wilson Wang Use of Polyphenol Tannic Acid to Functionalize Titanium with Strontium for Enhancement of Osteoblast Differentiation and Reduction of Osteoclast Activity Reprinted from: Polymers 2019 , 11 , 1256, doi:10.3390/polym11081256 . . . . . . . . . . . . . . . . 127 v Muzafar Khan, Gerd Heilemann, Wolfgang Lechner, Dietmar Georg and Andreas Georg Berg Basic Properties of a New Polymer Gel for 3D-Dosimetry at High Dose-Rates Typical for FFF Irradiation Based on Dithiothreitol and Methacrylic Acid (MAGADIT): Sensitivity, Range, Reproducibility, Accuracy, Dose Rate Effect and Impact of Oxygen Scavenger Reprinted from: Polymers 2019 , 11 , 1717, doi:10.3390/polym11101717 . . . . . . . . . . . . . . . . 145 John M. Warman, Matthijs P. de Haas, Leonard H. Luthjens, Tiantian Yao, Julia Navarro-Campos, S ̈ olen Yuksel, Jan Aarts, Simon Thiele, Jacco Houter and Wilco in het Zandt FluoroTome 1: An Apparatus for Tomographic Imaging of Radio-Fluorogenic (RFG) Gels Reprinted from: Polymers 2019 , 11 , 1729, doi:10.3390/polym11111729 . . . . . . . . . . . . . . . . 171 Huanan Yu, Xianping Bai, Guoping Qian, Hui Wei, Xiangbing Gong, Jiao Jin and Zhijie Li Impact of Ultraviolet Radiation on the Aging Properties of SBS-Modified Asphalt Binders Reprinted from: Polymers 2019 , 11 , 1111, doi:10.3390/polym11071111 . . . . . . . . . . . . . . . . 187 Xiangbing Gong, Zejiao Dong, Zhiyang Liu, Huanan Yu and Kaikai Hu Examination of Poly (Styrene-Butadiene-Styrene)-Modified Asphalt Performance in Bonding Modified Aggregates Using Parallel Plates Method Reprinted from: Polymers 2019 , 11 , 2100, doi:10.3390/polym11122100 . . . . . . . . . . . . . . . . 201 Guizhen Li and Kyung Ho Rwo Hydrophilic Molecularly Imprinted Chitosan Based on Deep Eutectic Solvents for the Enrichment of Gallic Acid in Red Ginseng Tea Reprinted from: Polymers 2019 , 11 , 1434, doi:10.3390/polym11091434 . . . . . . . . . . . . . . . . 215 Zhengwei Luo, Jiahuan Xu, Dongmei Zhu, Dan Wang, Jianjian Xu, Hui Jiang, Wenhua Geng, Wuji Wei and Zhouyang Lian Ion-Imprinted Polypropylene Fibers Fabricated by the Plasma-Mediated Grafting Strategy for Efficient and Selective Adsorption of Cr(VI) Reprinted from: Polymers 2019 , 11 , 1508, doi:10.3390/polym11091508 . . . . . . . . . . . . . . . . 231 vi About the Special Issue Editors Florian J. Stadler , Prof. Dr.-Ing. is distinguished professor at Shenzhen University, which he joined in 2014 after studies at the Friedrich-Alexander University Erlangen-Nuremberg (FAU), Germany and further stations in Japan, Belgium, and South Korea. His focus is on the research in polymer physics, especially rheology, polymer chemistry of functional polymers, and mostly metal oxide-based nanoparticles for environmental applications. He published more than 240 papers in a large variety of scientific journals. Bing Du , Dr. rer. nat., is lecturer of College of Materials Science and Engineering, Shenzhen University. She worked at Institute of Polymer Research from Helmholtz-Zentrum Geesthacht and received her Ph.D. degree in 2013. Her current research interests are development of polymer/carbon nano-composites, electrochemical sensors for detecting biomolecules, catalytic membrane reactor. vii polymers Editorial Functional Polymer Solutions and Gels—Physics and Novel Applications Bing Du and Florian J. Stadler * College of Materials Science and Engineering, Shenzhen Key Laboratory of Polymer Science and Technology, Guangdong Research Center for Interfacial Engineering of Functional Materials, Nanshan District Key Lab for Biopolymers and Safety Evaluation, Shenzhen University, Shenzhen 518055, China; dubing@szu.edu.cn * Correspondence: fjstadler@szu.edu.cn Received: 3 March 2020; Accepted: 16 March 2020; Published: 18 March 2020 Recent years have seen significant improvements in the understanding of functional soft matter. Advances in organic chemistry have identified a wide variety of possible interactions, ranging from hydrophobic interactions, e.g., based on cyclodextrin or hydrophobic end-capping, host–guest interactions, and multiple hydrogen bonding to metal–ligand bonding, such as for terpyridines and catechols. Those functional moieties can link polymer chains, usually in aqueous solution, and thus assemble these solutions into gels. These discoveries of the last ca. 30 years by chemists worldwide have made it possible to understand biological soft matter significantly better, as well as to create our own soft materials with tailored properties, such as a pH-controlled behavior. Their current and future applications are often focused on the biomedical field, particularly on drug release and tissue engineering. However, functional polymer solutions and gels can also be envisioned for many other applications. For example, functional nanofibers electrospun from solution can also be used for advanced applications. The resulting nanofibers combine an incredible highly specific surface area with an excellent performance as membranes with high flux, good separator selectivity, as well as extraordinary selective absorption for both functional nanoparticles and pollutants in water. This Special Issue of Polymers attracted contributions from several diverse fields of polymers which can only exemplarily illustrate the broadness of the topic of polymer solutions and gels. Polymers with special moieties, leading to thermoresponsive and stimuli-responsive behavior, was one of the main topics. Yan et al. [ 1 ] studied the interactions between tacticity of poly (N-iso-propylacrylamide) PNIPAM and 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl) imide ([BMIM][TFSI]) ionic liquid, in which a higher isotaxy of PNIPAM leads to a higher amount of interaction and, consequently, to more temperature stable gels, i.e., to an increased upper critical solution temperature. Interestingly, the results show that it is possible to have a decoupling of gelation and turbidity, which is counterintuitive and expands upon earlier knowledge on the physicochemical behavior of PNIPAM in ionic liquids [ 2 ]. These results show the relevance of ionic liquids for the solubilization of polymers, which has revolutionized the unwrapping of tightly packed crystalline cellulose [3–6]. Polymer solutions with catechol functionalities were shown to significantly influence thermoresponsive behavior as well as the end groups, which could be modeled statistically, demonstrating the combined e ff ects of the end groups derived from the rather hydrophobic RAFT agents and catechol groups [ 7 ], which has led to further elucidation as well as confirmed previous observations on the properties of thermoresponsive polymers containing catechol moieties [ 8 , 9 ]. This work also extends on previous reports on PNIPAM-based polymer with other structures [ 10 – 12 ]. Similarly to catechols, terpyridine groups—as one species of metal–ligand complexing functionalities—are used as a terminal group of self-assembling di-block copolymers which exhibit an unusually fast self-healing behavior as well as a highly concentration and ion-type-dependent rheology [13]. Polymers 2020 , 12 , 676; doi:10.3390 / polym12030676 www.mdpi.com / journal / polymers 1 Polymers 2020 , 12 , 676 Pure polymer physics was also represented in the theoretical study of Wang [ 14 ], which studied the drag reduction e ff ect in polymer solutions, an e ff ect which has been a focal point of interest for both experimental and theoretical polymer physicists for a long time [ 15 – 17 ], as drag reduction promises to be a technology that can contribute to the international climate crisis by reducing energy consumption for pumping fluids. The realm of environmental technology was represented by Luo et al. [ 18 ], who introduced a way to selectively adsorb highly environmentally polluting chromium (VI) ions that are often produced during leather production [ 19 ]. This work introduces a nonwoven able to adsorb chromium but also to release it and, thus, allowing for regeneration of the adsorbent. In comparison to many adsorption approaches based on nanoparticles, nonwovens have the advantage of macroscopic size and, thus, easier handling as a filter-like material. The biomedical applications in the Special Issue were represented by several contributions. Guan et al. [ 20 ] demonstrated the usability of alginate–acrylamide hydrogels for the production of vascular grafts—hydrogels that can be used for blood vessel repair, leading to similarly good mechanical performance as their natural porcine counterparts. Ste ffi et al. [ 21 ] developed a new way to improve bone-forming cell di ff erentiation by using a strontium-doped titania tannic acid polyphenol layer on titanium for implants. Such a coating of implants could improve the interface between the implant and the bone, especially in the case of osteoporosis. Skwira et al. [22] contributed to the Special Issue in the broad field of drug delivery with their paper investigating the release properties of ciprofloxacin antibiotic from special silica-based composites with ethylcellulose and polydimethylsiloxane. Li et al. [ 23 ] showed a biomedical-related use of hydrogels—they demonstrated how gallic acid (GA) could accumulate from red ginseng by adsorption on chitosan-based hydrogels. GA is a natural polyphenolic molecule, interesting for its antioxidant, anti-inflammatory, anticancer, and antiviral activities [24]. Khan et al. [ 25 ] showed one example of the use of polymer gels as dosimeters, providing a high-resolution equivalent of tissue in quality control of radiation therapy. Warman et al. [ 26 ] reported the development of a device for the tomographic imaging of radio-fluorogenic gels (RFGs), which allows for scanning the 3D distribution of radiation in a gel. Asphalt binders are another type of gel-like material covered in this Special Issue. Yu et al. [ 27 ] showed how e ffi ciently styrene–butadiene–styrene (SBS) tri-block copolymers are su ffi ciently UV-stable as an asphalt binder for permanently improving the properties of asphalt. Gong et al. [ 28 ] contributed to the same stream of research by investigating the rheological behavior of these asphalt–SBS mixtures, which complements a research line of polymer–asphalt mixtures for improving rheological properties [29,30]. Electrospinning technology is one of the most e ffi cient and straightforward approaches to fabricate the fibrous membrane or sca ff old [ 31 ]. Through the powerful tension, various solutions based on polymers or their composite are drawn and instantaneously solidified into micro- / nanoscale fibers. Owing to the nanoscale of the fibers, the electrospun products possess an extremely high ratio surface, conjunct network structure, and quite large porosity, providing plenty of possibilities to expand versatile materials. In particular, the fibrous structure can remarkably reduce the density of the materials; thus, it can e ff ectively “soften” the substance with a lightweight feature. Many researchers develop copious types of novel soft materials, which have been widely utilized for tissue sca ff old [ 32 , 33 ], wound dressing [ 34 ], fibrous membrane for catalyst [ 35 ], energy cell [ 36 ], and electrochemical [ 37 ] and mechanical [ 38 ] sensors. These active developments profit from the fascinating matrix based on nanofibrous structure, which extensively adapts to many fields as supporting materials. On the other hand, the electrospun membrane can also play a crucial role as one relative independent structural component because of its excellent intrinsic properties. In this Special Issue, Monteser í n et al. [ 39 ] reported on interesting layer-by-layer epoxy resin composites reinforced by electrospun nanofiber veils. They included electrospun material made of polyamide 6 modified with TiO 2 nanoparticles into carbon fiber / epoxy composite as a single structure. From this work, it was observed that the nanofibers 2 Polymers 2020 , 12 , 676 could e ff ectively improve the flexural stress at failure and fracture toughness of the composite. When the fibers were modified with TiO 2 , the composite exhibited new antibacterial performance, which widened the application of the material. The field of functional polymer solutions and gels has, so far, experienced a lot of attention from chemists, who are making numerous interesting, complex systems whose physical behavior is very complex. Hence, while polymer chemistry also including functional moieties has reached a certain level of maturity, main topics remain which are lacking a good understanding of the physics of such systems. The clear application direction for functional polymer solutions and gels is towards biomedical applications, which automatically means that the questions to be answered are rather complex as, in most cases, they involve interactions of complex functional polymer materials with even more complex—especially biological—systems. Classical polymer physics on melts and solutions without functional moieties has reached maturity after being intensively researched from ca. 1950 until the present date. Functional polymers were systematically introduced to research much later, and it will certainly take several decades until the same level of understanding is reached for the physics of functional polymers. The future of physics and applications of functional polymers will be highly diverse, as is shown in this Special Issue. We expect that special emphasis will be paid on tailoring the properties of the polymers to a particular application direction, as well as to gradually increase the fraction of modified natural polymeric systems in comparison to classical synthetic polymer systems. Functional polymer solutions and gels are often targeted for high-value applications, especially in the biomedical field. The complexities of these fields, owing to the multidimensional property profile of these materials interacting with very complex systems, also means that classical characterization methods are no longer su ffi cient for totally capturing the essential parameters of the system. As a consequence, we expect to see the development of combined methods, where two classical methods are merged together to yield 2 or more kinds of measurements simultaneously. Examples of these which the editors are familiar with include the combination of rheology with spectroscopic methods (nuclear magnetic resonance (NMR), Raman spectroscopy, Fourier transform infrared spectroscopy (FTIR), and dielectric spectroscopy). Furthermore, further improvement of existing methods will become necessary—one recent example being non-vacuum scanning electron microscopy (SEM), useful for investigating living biological samples or fast chip calorimetry, improving traditional speed limitations of dynamic scanning calorimetry of ca. 1–2 K / s by several orders of magnitude. Furthermore, we will see the development of completely new methods as well, which will suit needs of the scientific community. Lastly, as one of the primary areas of functional soft materials is the biomedical area, increasing collaborations with industrial partners will become necessary as the regulatory requirements for testing the safety of materials for in vivo use—i.e., applying the material to human or animal patients—are strongly regulated, requiring extensive and expensive tests that research institutions usually cannot pay for without strong support from industrial partners. Conflicts of Interest: The authors declare no conflicts of interest. References 1. Yan, Z.C.; Biswas, C.S.; Stadler, F.J. Rheological Study on the Thermoreversible Gelation of Stereo-Controlled Poly(N-Isopropylacrylamide) in an Imidazolium Ionic Liquid. Polymers (Basel) 2019 , 11 , 783. [CrossRef] [PubMed] 2. Biswas, C.S.; Stadler, F.J.; Yan, Z.-C. Tacticity e ff ect on the upper critical solution temperature behavior of Poly(N-isopropylacrylamide) in an imidazolium ionic liquid. Polymer 2018 , 155 , 101–108. [CrossRef] 3. 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[CrossRef] © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http: // creativecommons.org / licenses / by / 4.0 / ). 5 polymers Article Linear and Nonlinear Dynamic Behavior of Polymer Micellar Assemblies Connected by Metallo-Supramolecular Interactions Zhi-Chao Yan 1 , Florian J. Stadler 1,2, *, Pierre Guillet 2,3 , Cl é ment Mugemana 2,4 , Charles-Andr é Fustin 2 , Jean-François Gohy 2 and Christian Bailly 5 1 Shenzhen Key Laboratory of Polymer Science and Technology, Guangdong Research Center for Interfacial Engineering of Functional Materials, College of Materials Science and Engineering, Shenzhen University, Shenzhen 518060, China; yanzhch@szu.edu.cn 2 Institute of Condensed Matter and Nanosciences (IMCN), Bio and Soft Matter Division (BSMA), Universit é Catholique de Louvain, Place Pasteur 1, B-1348 Louvain-la-Neuve, Belgium; pierre.guillet@univ-avignon.fr (P.G.); clement.mugemana@list.lu (C.M.); charles-andre.fustin@uclouvain.be (C.-A.F.); jean-francois.gohy@uclouvain.be (J.-F.G.) 3 Equipe Chimie Bioorganique et Syst è mes Amphiphiles, Institut des Biomol é cules Max Mousseron (UMR 5247 UM-CNRS-ENSCM) & Avignon University, 301 rue Baruch de Spinoza, 84916 Avignon CEDEX 9, France 4 Luxembourg Institute of Science and Technology (LIST), 5 Avenue des Hauts-Fourneaux, 4362 Esch-sur-Alzette, Luxembourg 5 Institute of Condensed Matter and Nanosciences (IMCN), Bio and Soft Matter Division (BSMA), Universit é Catholique de Louvain, Place Croix du Sud 1, B-1348 Louvain-la-Neuve, Belgium; christian.bailly@uclouvain.be * Correspondence: fjstadler@szu.edu.cn Received: 13 August 2019; Accepted: 15 September 2019; Published: 20 September 2019 Abstract: The linear and nonlinear rheology of associative colloidal polymer assemblies with metallo-supramolecular interactions is herein studied. Polystyrene- b -poly( tert -butylacrylate) with a terpyridine ligand at the end of the acrylate block is self-assembled into micelles in ethanol, a selective solvent for the latter block, and supramolecularly connected by complexation to divalent metal ions. The dependence of the system elasticity on polymer concentration can be semi-quantitatively understood by a geometrical packing model. For strongly associated (Ni 2 + , Fe 2 + ) and su ffi ciently concentrated systems (15 w / v%), any given ligand end-group has a virtually 100% probability of being located in an overlapping hairy region between two micelles. By assuming a 50% probability of intermicellar crosslinks being formed, an excellent prediction of the plateau modulus was achieved and compared with the experimental results. For strongly associated but somewhat more dilute systems (12 w / v%) that still have significant overlap between hairy regions, the experimental modulus was lower than the predicted value, as the e ff ective number of crosslinkers was further reduced along with possible density heterogeneities. The reversible destruction of the network by shear forces can be observed from the strain dependence of the storage and loss moduli. The storage moduli of the Ni 2 + and Zn 2 + systems at a lower concentration (12 w / v%) showed a rarely observed feature (i.e., a peak at the transition from linear to nonlinear regime). This peak disappeared at a higher concentration (15 w / v%). This behavior can be rationalized based on concentration-dependent network stretchability. Keywords: associative polymer colloids; micellar assemblies; rheology 1. Introduction Supramolecular self-assembly is one of the most fascinating topics in soft matter. It gives synthetic materials some of the merits of biological systems, including self-healing properties, Polymers 2019 , 11 , 1532; doi:10.3390 / polym11101532 www.mdpi.com / journal / polymers 7 Polymers 2019 , 11 , 1532 response to external stimuli, and the ability to reversibly modify sti ff ness as a reaction to external stress levels [1–18] . Supramolecular self-assembly strategy has been shown to work excellently for constructing dynamically bonded gels [ 19 , 20 ]. In particular, supramolecular micellar gels can be created with somewhat slower dynamic behavior, according to a binary self-assembly strategy that combines both phase-separation-induced block aggregation and the bonding from supramolecular intermicellar interactions [ 7 ]. As regards micellar gels made by block copolymers, a kinetically controlled and even reversible self-assembly is possible, making these gels good candidates for self-repairing and injectable soft materials. So far, the research of supramolecular micellar gels is still mainly focused on chemically creating new functionality and designing new structures. The material’s physical properties have not yet been thoroughly evaluated, especially the relationship between rheological behavior and structural information like micelle size, intermicellar distance, relative volume of core and corona, and strength of supramolecular interactions. In an earlier study, the structure of a wormlike micelle supramolecularly bridged by telechelic polymers was explored by Ligoure et al. [ 6 ]. A similar approach was also conducted by Lodge et al. [ 21 , 22 ], who found evidence for establishing crosslinks between wormlike micelles by a poly(ethylene oxide) with alkyl stickers installed at the chain ends. However, their samples were mixtures of micelles and linear chains, which cannot answer the question in pure micellar gels of how supramolecular networks are formed simply by intermicellar bonding among arms in coronae. Among the di ff erent non-covalent interactions forming supramolecular bonds, the metal–ligand bond is particularly interesting because of its great directionality, broad selection of ligands, and easily tuned interaction strength that can be selected by choosing the appropriate metal ion. Guillet et al. [ 7 , 15 ] combined colloidal self-assembly and metallo-supramolecular interactions by exploring the behavior of polystyrene- b -poly( tert -butylacrylate) (PS- b -PtBA) with a terpyridine ligand at the end of the acrylate block, which is self-assembled in ethanolic solution. The addition of divalent ions such as Zn 2 , Ni 2 + , and Fe 2 + yield flower-like micelles in diluted solutions and temporary networks in concentrated and semi-concentrated systems. The connections formed by such micelles are shown in Scheme 1. The rheological behavior of such gels can be extensively tuned by choice of metal ion. Besides metal–terpyridine coordination, we have also reported interactions between dopamine and metal ions in thermosensitive copolymers for self-assembly into switchable polymer gels. This process depends on a variety of factors, including pH [ 23 , 24 ], temperature [ 23 ], solvent type [ 19 , 24 , 25 ], ion type [ 26 ], and nanoparticles [ 27 , 28 ]. In most studies, the rheological properties have been restricted to a few test setups. In these preliminary studies, a frequency sweep was often carried out to prove gelation at an almost constant phase angle δ (or a constant slope in storage and loss modulus) [ 20 , 29 ], while the absence of such a constant slope has indicated that the material is su ffi ciently elastic (as in the case of a typical entangled polymer) [ 30 ]. However, a relationship between these rheological results (e.g., the plateau modulus and structural and connecting situations of micelles) have not been theoretically established. In addition, the nonlinear rheological behavior of micellar gels has not been thoroughly explored. 8 Polymers 2019 , 11 , 1532 Scheme 1. Cartoon for connection formed by self-assembly of PS- b -PtBA with a terpyridine ligand. The core and coronae are PS and PtBA, respectively. Represents the metal ion. This paper expands on an understanding of the concentrated systems. It focuses on the surprising finding that even small concentration di ff erences can completely change rheological characteristics. Based on simple geometric considerations as well as structural and chemical information about this system, we first calculate a key structural parameter—the intermicellar linking fraction—then consider implications on gelling behavior. Predictions are compared with linear rheological measurements for two concentrations (12 and 15 w / v%) and three ions (zinc(II), iron(II), and nickel(II)). We further explore the transition from linear to nonlinear rheological behavior. 2. Experiments Preliminary results with these systems have previously been published [ 7 ]. The polymer is a polystyrene- b -poly( tert -butyl acrylate) (PS- b -PtBA) block copolymer with average polymerization degrees of 80 ( M n ≈ 8300 g / mol) and 200 ( M n ≈ 25,600 g / mol) for the PS and PtBA blocks, respectively, and a polydispersity index of 1.11 for the whole copolymer. The end of the PtBA block is functionalized with a terpyridine ligand. The diblock copolymer forms micelles in ethanol, with a glassy PS core and PtBA corona. As determined by static light scattering, these micelles have a radius of gyration of approximately 15 nm and contain 28 chains on average. Metal ions can be added to this suspension of hairy colloids following a procedure described elsewhere [ 7 ]. Up to two terpyridine ligands form complexes with the divalent metal ions used in this article (Fe 2 + , Ni 2 + , and Zn 2 + ), leading to supramolecular bonds either between chains from di ff erent micelles (forming crosslinks), or from the same micelle (forming loops) [ 7 ]. Three metal ions (Zn 2 + , Fe 2 + , and Ni 2 + ) are added as chloride salts. The quantity of ions is half an equivalent with respect to the terpyridine [7]. Small-angle x-ray scattering (SAXS) experiments were performed on station DUBBLE at the European Synchrotron Radiation Facility, Grenoble, France. The X-ray wavelength was λ = 1.55 Å. SAXS patterns were collected with a two-dimensional multiwire gas-filled detector. The wavenumber scale ( q = 4 π × sin θ / λ , where 2 θ is the scattering angle) was calibrated using a sample of wet collagen (rat tail tendon). The rheological characterization was performed with a TA Instruments ARES (New Castle, DE, USA) using either a 25 mm / 0.02 rad cone and plate geometry, a Malvern Kinexus (Malvern, Cambridge, UK) using a 25 mm / 0.5 ◦ cone, or a TA Instruments AR-G2 (New Castle, DE, USA) using a 40 mm / 2 or a 20 mm / 1 ◦ cone. The measurements were carried out at room temperature in an ethanol-saturated atmosphere to minimize evaporation of the solvent. All measurements were carried out at 20 ◦ C. Before measurement, an equilibration time of around 10 min was applied, which was found to be su ffi cient for all conditions. Dynamic frequency sweeps and nonlinear dynamic strain sweeps were also performed. 9 Polymers 2019 , 11 , 1532 3. Results 3.1. Structure of the Micellar Network To explain the rheological data, the results of the analytical characterization are essential. Figure 1