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Yoshika Kimura, Asuka Murao, Tomoya Tashiro, Noboru Osaka, Yuji Kamiyama, [Takeshi Ueki](https://orcid.org/0000-0001-9317-6280), [Kenta Fujii](https://orcid.org/0000-0003-0057-1295)

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[Metal–Polymer Soft Framework Ion Gels: Linking Coordination Chemistry to Macroscopic Elasticity](https://mdr.nims.go.jp/datasets/e055bb91-2f07-4eef-a4a3-c3733d3990ac)

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Metal–Polymer Soft Framework Ion Gels: Linking Coordination Chemistry to Macroscopic ElasticityMetal−Polymer Soft Framework Ion Gels: Linking CoordinationChemistry to Macroscopic ElasticityYoshika Kimura,# Asuka Murao,# Tomoya Tashiro, Noboru Osaka, Yuji Kamiyama, Takeshi Ueki,*and Kenta Fujii*Cite This: Chem. Mater. 2026, 38, 5723−5731 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Linking molecular interactions to the macroscopic mechanical proper-ties of soft materials remains a major challenge in soft-matter science. Here, we developmetal−polymer soft framework (MPF) ion gels, in which metal−ligand coordinationcomplexes function as network-forming interchain bridges within a structurallyhomogeneous polymer network. Terpyridine-terminated TetraPEG prepolymers werecross-linked with divalent metal ions in an ionic liquid to form uniform coordination-bonded gel networks. The elastic modulus (G′) increased in the order Mg2+ < Zn2+ <Co2+ < Ni2+, and this trend was quantitatively reproduced by modeling the equilibriumdistribution of bis-terpyridine complexes, M(tpy)22+, acting as network-forminginterchain bridges in the polymer network. By integrating coordination thermodynamics with classical rubber elasticity, weestablished a quantitative framework that determines the stepwise equilibrium constants (K1 and K2) for mono- and bis-terpyridinecomplex formation and accurately predicts the nonmonotonic dependence of G′ on metal-ion concentration. Furthermore, the stressrelaxation time (τ) was found to increase with increasing coordination bond strength, indicating that the dynamic mechanicalresponse is correlated with the strength of metal−ligand interactions. These results establish a quantitative framework linkingcoordination thermodynamics with macroscopic gel elasticity and further suggest that coordination interactions also play animportant role in controlling the dynamic mechanical response, providing a basis for tuning the properties of coordination-bondedsoft materials.■ INTRODUCTIONUnderstanding how microscopic molecular interactions governmacroscopic mechanical properties remains a central challengein soft-matter chemistry.1−3 In polymer networks, elasticityand relaxation dynamics emerge from the collective responseof countless transient and permanent cross-links.1,4 Establish-ing a quantitative and predictive connection between thecollective behavior of molecular bonds and the bulk mechanicsof soft materials would transform the design of polymernetworks from empirical optimization to molecular-levelengineering.Ion gels, polymer networks swollen with ionic liquids (ILs),provide a particularly attractive platform for exploringmolecular design principles.5−8 The IL component is not aninert solvent but a functional liquid that can impart ionicconductivity, (electro)chemical stability, and thermal stabilityto otherwise purely mechanical polymer networks.9−13 Whenconfined within the nanoscopic space of the network, the ILbehaves as a “liquid guest” whose physicochemical function-ality coexists with, yet is distinct from, the mechanical role ofthe polymer framework. In this sense, the ion gel represents ahybrid soft framework in which the polymer network dictatesmechanical integrity, while the encapsulated IL contributesadditional physicochemical functions.Metal−ligand coordination chemistry offers an idealmolecular handle to bridge chemical bonding and macroscopicmechanics within such hybrid frameworks.14−16 The reversibleformation and dissociation of coordination bonds providedynamic cross-linking points whose thermodynamic andkinetic parameters are well-defined. Hydrogels and ion gelsincorporating coordination bonds, typically through catechol,bipyridine, or terpyridine ligands, have thus been explored asdynamic polymer networks exhibiting self-healing, stressrelaxation, and tunable viscoelasticity.15,17−24 Yet, most ofthese studies have been qualitative, correlating mechanicaltrends with the choice of metal ion, rather than quantitativelylinking coordination chemistry to macroscopic elasticity andrelaxation. A critical requirement for achieving such aquantitative relationship is a polymer network with molec-ular-level structural uniformity. Conventional polymer gelsoften suffer from inhomogeneous cross-linking and chain-length distributions, which blur the direct correspondenceReceived: March 21, 2026Revised: May 10, 2026Accepted: May 12, 2026Published: May 20, 2026Articlepubs.acs.org/cm© 2026 The Authors. Published byAmerican Chemical Society5723https://doi.org/10.1021/acs.chemmater.6c00832Chem. Mater. 2026, 38, 5723−5731This article is licensed under CC-BY 4.0Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on June 10, 2026 at 02:39:23 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Yoshika+Kimura"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Asuka+Murao"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Tomoya+Tashiro"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Noboru+Osaka"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Yuji+Kamiyama"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takeshi+Ueki"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenta+Fujii"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenta+Fujii"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.chemmater.6c00832&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=agr1&ref=pdfhttps://pubs.acs.org/toc/cmatex/38/11?ref=pdfhttps://pubs.acs.org/toc/cmatex/38/11?ref=pdfhttps://pubs.acs.org/toc/cmatex/38/11?ref=pdfhttps://pubs.acs.org/toc/cmatex/38/11?ref=pdfpubs.acs.org/cm?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c00832?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/cm?ref=pdfhttps://pubs.acs.org/cm?ref=pdfhttps://creativecommons.org/licenses/by/4.0/between molecular-scale events and bulk mechanical re-sponse.25−27 In sharp contrast, tetra-arm poly(ethylene glycol)(TetraPEG) forms a nearly ideal, homogeneous network inwhich the density and spatial arrangement of cross-linkingjunctions are statistically uniform.28−34 In addition, using anonvolatile IL as the solvent ensures that both the polymerconcentration and the coordination equilibria remain constantthroughout the measurements. This compositional stabilityunder fully closed conditions enables a consistent andquantitative linkage between molecular coordination chemistryand macroscopic mechanical response without compositionaldrift, something difficult to achieve in conventional solventsystems such as water or organic media. Owing to thisstructural uniformity, TetraPEG can form not only hydrogelsbut also organogels and ion gels swollen with organicelectrolytes or ILs, while maintaining well-defined andreproducible network structures even in nonaqueousmedia.35−38 This structural precision allows the mechanicalproperties to be interpreted solely in terms of the chemicalnature and dynamics of the cross-links, without structuralambiguity.Here, we present metal−polymer soft framework (MPF) iongels that integrate a structurally well-defined polymer networkwith coordination-bonded interchain bridges and a functionalIL environment. Terpyridine-terminated TetraPEG (Tetra-PEG-tpy) prepolymers were cross-linked via complexationwith metal ions (Ni2+, Co2+, Zn2+, and Mg2+) in an IL medium.The tpy ligand was selected because its tridentate coordinationenables the formation of highly stable octahedral M(tpy)2complexes (1:2 metal-to-ligand ratio) with divalent metal ions,particularly first-row transition metal ions. This geometryallows the tetrafunctional TetraPEG chains to form idealtetrahedral (diamond-lattice-like) network junctions, providinga structurally well-defined polymer network. Owing to the highhomogeneity of the TetraPEG network and the well-characterized equilibrium of metal-terpyridine complexation,this system provides a quantitative platform to correlatecoordination chemistry with macroscopic mechanics. Theelastic modulus is governed by the equilibrium concentrationof bis-terpyridine complexes, M(tpy)22+, which function asnetwork-forming interchain bridges in the polymer network. Inthe context of rubber elasticity, these bridges correspond toelastically active junctions that contribute to the macroscopicelastic modulus, while the stress-relaxation time reflects theeffective lifetime associated with network rearrangementmediated by dynamic metal−ligand coordination.By unifying thermodynamic and kinetic descriptions ofcoordination interactions within a homogeneous polymerscaffold, we establish a molecular-level framework thatquantitatively links coordination chemistry to the mechanicalbehavior of soft materials. This approach demonstrates howthe elasticity and relaxation of ion gels can be chemicallypredicted from the equilibrium and dynamics of theirinterchain-bridge motifs while simultaneously retaining theunique functionalities of an IL-based medium.■ EXPERIMENTAL SECTIONMaterials1-Ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide([C2mIm][TFSA]; Kanto Chemical) was used as received withoutfurther purification. The water content of the IL was confirmed to bebelow 100 ppm by Karl Fischer titration. Hydroxyl-terminated tetra-arm poly(ethylene glycol) (TetraPEG−OH, Mw = 20,000 g mol−1;SINOPEG) and 4′-chloro-2,2′:6′,2″-terpyridine (Tokyo ChemicalIndustry), which served as the chelating ligand for end-groupmodification, were also used without further purification. Zinc(II)and Magnesium(II) bis(trifluoromethanesulfonyl)amide (Zn(TFSA)2and Mg(TFSA)2; Tokyo Chemical Industry) were used as purchased,whereas Nickel(II) and Cobalt(II) bis(trifluoromethanesulfonyl)-amides (Ni(TFSA)2 and Co(TFSA)2) were synthesized accordingto the following procedure. Basic metal carbonates (MCO3·2M-(OH)2·4H2O, M = Ni or Co, 25 mmol; Kanto Chemical orFUJIFILM Wako Pure Chemical) were dissolved in an aqueoussolution of bis(trifluoromethanesulfonyl)amide acid (HTFSA, 180mmol, 30 mL; Tokyo Chemical Industry). The mixture was stirred for5 h, followed by three repetitions of recrystallization and vacuumfiltration. The obtained solids were dried under vacuum for 2 days toafford the corresponding M(TFSA)2 salts.Preparation of TetraPEG-Based MPF Ion GelsIn this system, the coordination between metal ions and terpyridine-functionalized TetraPEG connects multiple polymer arms to form apercolated polymer network, in which the resulting metal−ligandcomplexes function as network-forming interchain bridges, analogousto well-defined network formation in tetra-functional polymersystems.28,32,34 The coordination-bonded TetraPEG ion gels weresynthesized through a two-step process:39 terminal functionalizationof TetraPEG−OH with terpyridine (tpy) ligands, followed by gelationvia coordination complex formation between metal ions (M2+) andthe tpy ligands in an ionic liquid (IL), as illustrated in Figure 1. Thedetailed procedure is as follows: (Step 1) TetraPEG−OH (Mw =20,000 g mol−1, 0.05 mmol) was dissolved in dimethyl sulfoxide(DMSO, 8 mL) in the presence of KOH (0.16 g, 3 mmol). Under anAr atmosphere, 4′-chloro-2,2′:6′,2″-terpyridine (0.16 g, 0.6 mmol)was added to the solution, and the mixture was stirred at 333 K for 48h to obtain the TetraPEG−tpy prepolymer. The resulting solutionwas poured into cold water to precipitate unreacted terpyridine, whichwas removed by vacuum filtration. The obtained DMSO solutioncontaining TetraPEG−tpy was transferred into a cellulose dialysismembrane and dialyzed against deionized water for 7 days to removeresidual DMSO and KOH. The resulting aqueous TetraPEG−tpysolution was concentrated and dried under reduced pressure, and thesolid product was further purified by precipitation using tetrahy-drofuran (THF) as a good solvent and diethyl ether (DEE) as a poorsolvent. The yield of the synthesized TetraPEG−tpy was 65.2%. Theterminal modification ratio, determined by 1H NMR, was 97.6%,confirming that the hydroxyl groups of TetraPEG−OH were almostcompletely functionalized with terpyridine ligands (details areprovided in the Supporting Information, Figure S1). (Step 2) IL([C2mIm][TFSA]) was used as the solvent herein to prepare two IL-based solutions: a TetraPEG−tpy/IL solution and a metal ion/ILsolution containing M(TFSA)2 (M = Ni, Co, Zn or Mg). To controlFigure 1. Schematic illustration of the synthesis procedure forTetraPEG-based MPF ion gels.Chemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c00832Chem. Mater. 2026, 38, 5723−57315724https://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig1&ref=pdfpubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c00832?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asthe gelation time, a small amount of HTFSA was added to theTetraPEG−tpy/IL solution. The molar ratios of HTFSA to terminaltpy units were adjusted to approximately 2:1 (0.03 M). In contrast, noHTFSA was added to the Mg2+ system because gelation did notproceed in the presence of HTFSA. Both IL solutions were mixed atroom temperature, during which spontaneous complexation betweenM2+ ions and terminal tpy ligands occurred, leading to the formationof transparent TetraPEG-based MPF ion gels. The polymerconcentrations of the prepared ion gels were 5, 10, and 15 wt %,and the M2+ ion concentrations ranged from 7.6 to 46 mM.Experimental MethodsMechanical stretching measurements were performed using dumbbell-shaped samples (rectangular portion: 2.0 × 12.0 × 2.0 mm3) of theTetraPEG-based MPF ion gels at a constant stretching velocity of 30mm min−1 using a mechanical testing apparatus (STB-1225S; A&DCompany). Rheological measurements of the ion gels were performedusing a stress-controlled rheometer (MCR-302; Anton Paar)equipped with a parallel-plate geometry (PP-25; 25 mm diameter),as follows. First, the IL solution containing metal salts and dissolvedTetraPEG−tpy prepolymer was placed between the plates, and thetime dependence of the storage (G′) and loss (G″) moduli during thegelation process was recorded at 298 K. The frequency and strainwere set to 1 Hz and 1%, respectively. After confirming the gelationcompletion time, defined as the point at which G′ reached a constantplateau value (see Figure S2), the frequency dependence and stressrelaxation of the fully gelled ion gel were subsequently measuredunder the same configuration. In the frequency-dependence measure-ments, the angular frequency was varied from 0.1 to 100 rad s−1 at astrain amplitude of 1%. Stress relaxation measurements wereperformed under the same parallel-plate configuration. A constantstrain of 1% was applied, and the decay of the stress was monitoreduntil the relaxation process reached completion. The measurementswere conducted at different temperatures: 293, 323, and 353 K for theNi2+ system, and 293 K for the Co2+, Zn2+, and Mg2+ systems. Small-angle X-ray scattering (SAXS) measurements were performed at theBL40B2 beamline of SPring-8 (Hyogo, Japan). The X-ray wavelengthand camera length were set to 0.10 nm and 4288.2 mm, respectively.The measurements were conducted at room temperature (ca. 298 K)using a PILATUS3 S 2 M (Dectris Ltd., Baden, Switzerland) detectorwith an exposure time of 30 s. Repeated measurements confirmed theabsence of radiation damage. The sample solutions were gelled in situwithin quartz capillaries (Hilgenberg GmbH, Malsfeld, Germany)with a diameter of 1 mm and used for the measurements. Theobtained scattering data were normalized by the exposure time,transmittance, and sample thickness. Background scattering from thecapillary and the IL (solvent) was subtracted, taking into account thevolume fraction of the IL. Density functional theory (DFT)calculations were performed using the Gaussian 09 softwarepackage.40 Geometry optimizations for the M−tpy complexes, aswell as for the isolated M2+ ions and tpy ligands, were carried out atthe M06/def2-TZVP level of theory, followed by normal frequencyanalyses to confirm that all optimized structures corresponded to trueenergy minima without any imaginary frequencies. The bindingenergies (ΔEbind) were evaluated as the electronic energy differencebetween the optimized complex and the sum of its constituentcomponents (M2+ and tpy), without applying any basis-set super-position error (BSSE) correction, according to the following equation,defined as ESCF (complex) − ESCF (M2+) − 2ESCF (tpy). High-spinstates were used for Ni2+ (triplet, d8) and Co2+ (quartet, d7), and asinglet for Zn2+ (d10) and Mg2+.■ RESULTS AND DISCUSSIONMechanical PropertiesTo understand how the static mechanical properties of theMPF gels arise from the equilibrium state of coordinationinterchain bridges, we first examined their macroscopicelasticity. Because the network topology of TetraPEG is nearlyideal, variations in elasticity can be attributed primarily tochanges in the population of metal−ligand complexes ratherthan to structural heterogeneity. Figure 2a shows the stress−elongation (σ−λ) curves of the TetraPEG-based MPF ion gelscross-linked with Ni2+ ions. The measurement was performedon fully gelled samples, after confirming gelation completion,defined as the point where G′ reached a constant plateau value(see Figure S2). The polymer concentrations were 5, 10, and15 wt %, and the molar ratio of metal ions to terminal tpyligands was fixed at cM/ctpy = 0.5. The stress σ graduallyincreased with increasing elongation ratio λ, and the breakingstress (σmax) reached 9.4 kPa for the 5 wt % ion gel (maximumelongation, λmax = 2.0), 72.8 kPa for the 10 wt % gel (λmax =3.4), and 99.4 kPa for the 15 wt % gel (λmax = 2.8),respectively. The Young’s modulus (E) was determined fromthe initial slope of the σ−λ curves and found to be 9.3, 52.1,and 115.3 kPa for the ion gels with polymer concentrations of5, 10, and 15 wt %, respectively. Figure 2b shows the storage(G′) and loss modulus (G″) as a function of frequency (ω)obtained for the TetraPEG-based MPF ion gels. At all polymerconcentrations examined, the G′ values remained nearlyconstant over the measured ω range and were consistentlyhigher than the corresponding G″ values. This behaviorcorresponds to a typical rubbery plateau, indicating that theformed M2+−tpy complexes acting as network-forminginterchain bridges are stable within the experimental timescale, confirming the elastic network structure of the gels. TheFigure 2. (a) Stress−elongation (σ−λ) curves of TetraPEG-based MPF ion gels cross-linked by Ni2+−tpy complexation, measured at polymerconcentrations of 5, 10, and 15 wt %. The molar ratio of metal ions to total terminal tpy units was fixed at cM/ctpy = 0.5. (b) Storage (G′, filledcircles) and loss (G″, open circles) moduli as a function of frequency for the same ion gels. (c) Dependence of Young’s modulus (E, black circles)and shear modulus (G′, red triangles) on polymer concentration.Chemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c00832Chem. Mater. 2026, 38, 5723−57315725https://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig2&ref=pdfpubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c00832?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asdependence of the Young’s modulus (E) and storage modulus(G′) on polymer concentration is summarized in Figure 2c.Both values exhibited a linear relationship with polymerconcentration, indicating that the elastic modulus of the iongels is directly controlled by the polymer concentration, that is,by the density of elastically active junctions. Furthermore, theratio of E to G′ (E ≈ 3G′) was close to the theoretical valueexpected for isotropic elastic networks, implying that thecoordination-bonded polymer network is nearly homogeneous.In addition, previous studies on TetraPEG in [C2mIm][TFSA]have shown that the overlap concentration (c*) is approx-imately 4−5 wt % for Mw ≈ 20 000 g mol−1 and scales as c* ∝Mw−4/5.41 Because the polymer concentrations employed inthis study are at or above this range, the polymer chains areexpected to be in the overlap regime, where intermolecularinteractions and network formation are possible. This isconsistent with the observed development of elasticity withincreasing polymer concentration. In this concentrationregime, a percolated network is formed, which enables theemergence of macroscopic elasticity. This interpretation isfurther supported by small-angle X-ray scattering (SAXS)measurements (see the Supporting Information: Figure S3 andTable S1), which confirm the network homogeneity of thepresent MPF ion gels, in good agreement with previous reportson chemically interchain-bridged TetraPEG ion gels (FigureS3a).35,41 No scattering peak arising from network inhomoge-neity was observed; instead, all MPF ion gels examined hereinexhibited a monotonic q−2-dependence (q: scattering vector),well described by the Ornstein−Zernike function, which ischaracteristic of homogeneous TetraPEG networks.29,35,41,42This scattering profile was retained irrespective of the metal-ion species or polymer concentration (Figures S3b and S3c,respectively).Figure 3 shows the variation in the G′ values of 5 wt %TetraPEG-based MPF ion gels as a function of metal ionconcentration (cM) for M2+ = Ni2+, Co2+, Zn2+, and Mg2+. Thefrequency-dependent data used to determine these G′ valuesare provided in Figure S4. For the transition metal ions, the G′values increased in the order Zn2+ < Co2+ < Ni2+. This trend isconsistent with the order of the thermodynamic stability of theM−tpy complexes, as reflected in their equilibrium formationconstants, which qualitatively parallels the ligand fieldstabilization energy (LFSE) sequence. For example, for theaqua complexes [M(H2O)6]2+, the degree of stabilizationincreases in the order Zn2+ (0 kJ mol−1) < Co2+ (−89 kJmol−1) < Ni2+ (−122 kJ mol−1) calculated based on the ligand-field splitting energy (10 Dq);43 see the SupportingInformation for details. These differences in stability aredirectly reflected in variations in the equilibrium distribution ofthe M−tpy complexes that function as network-forminginterchain bridges, as discussed later.When Li+ ions were used as the central metal ions in theTetraPEG−tpy/IL system, no gelation occurred (Figure S5)because the Li−tpy interaction is essentially electrostatic,lacking the orbital overlap required for coordination bonding;as a result, the Li−tpy complex is not stably formed. Incontrast, Mg2+ ions induced gelation, and the resulting G′ waslower than that of the Zn2+ system (Figure 3, green). AlthoughMg2+ lacks d orbitals for strong orbital overlap, its highercharge density compared to Li+ leads to stronger electrostaticinteractions with the tpy ligand, allowing the formation ofcoordination complexes sufficient to generate a percolatednetwork.When examining the dependence on the metal ionconcentration (cM), all M2+ systems exhibited a similar trend:the G′ value increased sharply up to approximately 10 mM,followed by a gradual decrease beyond this concentration. Torationalize this behavior, a quantitative analysis was conductedby considering the complexation equilibrium governing theformation of the M−tpy complexes.Quantitative Analysis of Gel Elasticity Based onMetal−Ligand Complexation EquilibriumIn the coordination-bonded MPF ion gels investigated in thisstudy, the concentration of network-forming interchain bridges(M−tpy complexes), which directly determines the elasticmodulus, can be described based on the complexationequilibrium between the metal ions and terpyridine ligands.Similar approaches have been reported for metal-coordinatedhydrogel systems, where quantitative relationships betweencoordination equilibria and macroscopic elasticity have beenestablished. In such systems, the concentration of elasticallyactive junctions has been predicted using equilibrium constantsfor metal−ligand complexation determined in aqueoussolutions together with the acid dissociation constant of theligand (pKa).19,44 In contrast, in IL systems, experimentaldetermination of metal−ligand complexation equilibria re-mains highly challenging, and experimental equilibriumconstants are rarely available.The complexation reaction between the metal ions (M2+)and terpyridine (tpy) ligands proceeds in two successive steps:M tpy M(tpy)2 2V++ +M(tpy) tpy M(tpy)222V++ +The stepwise formation constants are defined asK M(tpy) /( M tpy )12 2= [ ] [ ][ ]+ +andK M(tpy) /( M(tpy) tpy )2 22 2= [ ] [ ][ ]+ +Here, M(tpy)2+ and M(tpy)22+ are referred to as the mono-and bis-complexes, respectively, and the latter functions as anelastically active junction in the network. The total metal ionconcentration is given by cM = [M2+] + [M(tpy)2+] +[M(tpy)22+]. By solving these mass-balance equations, theconcentration distribution of each metal species (free M2+,Figure 3. Storage modulus (G′) of 5 wt % TetraPEG-based MPF iongels as a function of metal ion concentration (cM) for M2+ = Ni2+,Co2+, Zn2+, and Mg2+.Chemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c00832Chem. Mater. 2026, 38, 5723−57315726https://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig3&ref=pdfpubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c00832?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asM(tpy)2+ complex, and M(tpy)22+ complex) can be obtained.The concentration of the M(tpy)22+ complex, which acts as theinterchain bridge in the gel network, is expressed asK KK K KcM(tpy)tpy1 tpy tpy22 1 221 1 22 M[ ] = [ ]+ [ ] + [ ]+(1)In the present MPF ion gel system, however, thecomplexation equilibrium must be considered together withthe acid−base equilibrium of the tpy ligand, because a strongacid (HTFSA) was added to control the gelation kinetics.Terpyridine can be protonated according to the equilibrium:tpy + H+ ⇄ Htpy+, where the acid dissociation constant of theprotonated terpyridine species (Htpy+) is defined as Ka =[H+][tpy]/[Htpy+]. As a result, only the deprotonated tpyspecies is available for coordination with metal ions.Accordingly, the total concentration of tpy ligands wasexpressed as ctpy = [tpy] + [Htpy+] + [M(tpy)2+] +2[M(tpy)22+] = 15 mM, which corresponds to the concen-tration of terminal tpy groups in the 5 wt % MPF ion gels. Thetotal proton concentration was expressed as cH = [H+] +[Htpy+], where cH is the concentration of added HTFSA (0.03M). By combining the acid−base equilibrium, the proton massbalance, and the metal−ligand complexation equilibria, thefollowing equation for the free tpy concentration [tpy] wasobtained:ccKK K KK K Kctpytpytpytpy 2 tpy1 tpy tpytpyHa1 1 221 1 22 Mikjjjjjy{zzzzz= [ ] + [ ]+ [ ]+ [ ] + [ ]+ [ ] + [ ](2)Because ctpy and cM are fixed experimental parameters, eq 2represents a nonlinear equation with respect to the [tpy] andwas therefore solved numerically for each cM. The physicallymeaningful solution satisfying 0 ≤ [tpy] ≤ ctpy was selected andthe obtained [tpy] value was then substituted into eq 1 tocalculate the concentration of the bis-terpyridine complex,[M(tpy)22+], which contributes to network connectivity andfunctions as an elastically active junction within the MPF iongel network.Using the resulting concentration of M(tpy)22+, the elasticmodulus of the MPF ion gels was quantitatively analyzed basedon classical rubber elasticity theory. The elasticity of the gels isexpressed by the classical rubber elasticity relation (affinenetwork model), G = νRT, where ν (mol m−3) is the effectivemolar density of network strands, T (K) is the absolutetemperature, and R (J K−1 mol−1) is the gas constant (R = NAk,with NA and k being Avogadro’s and Boltzmann’s constants,respectively). For the present MPF ion gels, ν was calculatedfrom the reaction efficiency (or conversion) p between themetal ions and tpy ligands, based on the tree-like networktheory.30 The p, defined as the concentration ratio of tpyligands within bis-tpy complexes to total terminal tpy (i.e., p =2[M(tpy)22+]/ctpy), was evaluated from the equilibriumdistribution of the free M2+, mono-, and bis-tpy complexes,calculated from K1 and K2. The ν was then determined from paccording to the tree-like network model,30 as described indetail in the Supporting Information. Here, it should be notedthat the modulus of a polymer gel is influenced not only by thenetwork connectivity but also by polymer−solvent inter-actions. Recent studies on ideal homogeneous TetraPEGhydrogels have revealed that water molecules contribute to theenergy elasticity through hydration effects, leading to “negativeenergy elasticity” that reduces G′.45−49 Therefore, in thepresent ion gel systems, the polymer−IL interactions must alsoFigure 4. (a−d) Experimental storage moduli (G′; symbols) and calculated curves (solid lines) for 5 wt % TetraPEG-based MPF ion gelscontaining (a) Ni2+, (b) Co2+, (c) Zn2+, and (d) Mg2+ ions. The calculated curves were obtained from the equation: Gcalc = ανRT, using theoptimized equilibrium constants. The numerical values shown in each panel represent the molar ratio of total metal ions to total terminal tpyligands (cM/ctpy: 0.5−3), corresponding to cM = 7.6−46 mM. (e−h) Equilibrium species distributions of the free metal ions (M2+, light gray),monotpy complexes (M(tpy)2+, gray), and bis-tpy complexes (M(tpy)22+, black) in the ionic liquid medium, obtained using the optimizedequilibrium constants for (e) Ni2+, (f) Co2+, (g) Zn2+, and (h) Mg2+ systems. The molar fractions of each species (xM, xM(tpy), and xM(tpy)2) weredefined as follows: xM = 1/(1 + K1[tpy] + K1K2[tpy]2); xM(tpy) = K1[tpy]/(1 + K1[tpy] + K1K2[tpy]2); xM(tpy)2 = K1K2[tpy]2/(1 + K1[tpy] +K1K2[tpy]2). The vertical lines indicate the equilibrium points at which the total tpy concentration, ctpy = [tpy] + [Htpy+] + [M(tpy)2+] +2[M(tpy)22+] = 15 mM, is satisfied for each cM/ctpy ratio.Chemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c00832Chem. Mater. 2026, 38, 5723−57315727https://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig4&ref=pdfpubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c00832?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asbe considered. To account for such effects, the calculatedmodulus was defined asG RTcalc = (3)where α is an empirical correction factor that compensates fordeviations from ideal rubber elasticity arising from polymer−ILinteractions and the highly ionic environment, and Gcalccorresponds to the experimentally observed G′. The value ofα was determined using a chemically cross-linked TetraPEGion gel (polymer concentration: 5 wt %) prepared via aMichael addition reaction between thiol- and maleimide-terminated TetraPEG prepolymers36,38,45 in [C2mIm][TFSA]ionic liquid. From the experimentally measured modulus(G′chem, Figure S6) and the effective molar strand density(νchem), α was calculated as α = G′chem/(νchemRT). The νchemwas estimated based on the tree-like theory using polymerconcentration and reaction efficiency p (determined from time-dependent UV−vis spectroscopy; Figure S7), as detailed in theSupporting Information. Using the obtained νchem, the α valuein [C2mIm][TFSA] was determined to be 0.58. With this αvalue, the equilibrium constants K1, K2, and Ka were optimizedby least-squares fitting of the experimental storage moduli(Gexp, = G′) to the calculated values (Gcalc), by minimizing theresidual sum of squares, Σ[Gexp − Gcalc]2. In the fitting, theinitial value of Ka was set to pKa ≈ 10, based on the knownshift of acid−base equilibria toward higher pKa values in[C2mIm][TFSA] relative to aqueous solutions, as reported inour previous potentiometric titration studies in the ILsystem.50,51 The optimized pKa values remained close to thisinitial estimate, indicating that the fitting was not overlysensitive to Ka. The resulting fitted curves and the experimentaldata are shown in Figure 4.Figures 4a−4c present the experimentally measured G′(symbols) and calculated G curves (solid lines) for the 5 wt %TetraPEG-based MPF ion gels containing Ni2+, Co2+, andZn2+, respectively. The calculated results successfully repro-duced the experimental data for all M2+ systems, yielding theoptimized equilibrium constants: logK1 = 11.0, logK2 = 12.3,and pKa = 10.1 for Ni2+; logK1 = 11.1, logK2 = 12.0, and pKa =10.2 for Co2+; logK1 = 11.2, logK2 = 11.4, and pKa = 10.1 forZn2+. The Mg2+ system also showed good agreement betweenthe experimental and calculated G′ vs cM profiles (Figure 4d),and the equilibrium constants were determined to be log K1 =2.3 and log K2 = 2.5. These values are summarized in Table S2,together with literature values for aqueous systems forcomparison. Compared with aqueous systems, the pKa andcomplexation constants (logK1, logK2) in the IL areappreciably larger, indicating that both ligand deprotonationand metal−ligand coordination are substantially enhanced.These results reflect the specific solvation and coordinationenvironment in ILs. Notably, this work provides a quantitativeframework to determine these equilibrium constants in ILsystems by combining equilibrium analysis with macroscopicelasticity, which has not been established previously.The corresponding equilibrium distributions of the free M2+,M(tpy)2+, and M(tpy)22+ species calculated using theseoptimized constants are shown in Figure 4e−h. For all theM2+ systems, the bis-complex M(tpy)22+ predominates in thelow metal ion concentration region (cM ∼ 7.6−10 mM,corresponding to cM/ctpy ratios of 0.5−0.65). As cM increases,the equilibrium shifts toward dissociation, leading to thedominance of monocomplex and free M2+ species. Con-sequently, the number of interchain bridges decreases,resulting in a reduction of G′. Indeed, when the concentrationof the bis-terpyridine complex, [M(tpy)22+], calculated fromthe optimized equilibrium constants, is plotted as a function ofcM (Figure S8), the resulting profiles directly correspond to thecM-dependence of G′ shown in Figure 4a−d for all metal ionsystems. The overall trend in G′ (Mg2+ < Zn2+ < Co2+ < Ni2+)is also consistent with the sequence of the attainableconcentration of M(tpy)22+ determined by the equilibriumconstants.Furthermore, because the formation of M(tpy)22+ dependson the overall stoichiometric ratio of metal ions to tpy ligands(cM/ctpy), the static mechanical properties of the MPF ion gelscan be systematically tuned by adjusting this ratio, whichprovides a quantitative molecular basis for elasticity control incoordination-bonded polymer networks. These observationsdemonstrate that the equilibrium distribution of mono- andbis-tpy complexes directly governs the macroscopic stiffness ofthe MPF ion gels. This quantitative correspondence highlightsthat static elasticity can be predicted from coordinationthermodynamics alone, a level of control rarely achieved inconventional polymer networks.Role of Coordination Bond on Stress Relaxation BehaviorWhile the equilibrium concentration of coordination com-plexes determines the static elasticity, the dynamic mechanicalresponse of the MPF gels is closely related to the nature ofcoordination bonding.52,53 To explore this connection, weanalyzed the stress relaxation behavior of the MPF ion gels,which sensitively captures the time scale of bond dissociationand reformation. Figure 5a shows the stress relaxation curvesobtained for the 5 wt % TetraPEG-based MPF ion gels at cM =7.6 mM (cM/ctpy = 0.5). Under the experimental condition(strain amplitude, 1%), the MPF ion gels (Ni2+, Co2+, Zn2+,and Mg2+ systems) were confirmed to exhibit linear viscoelasticbehavior, via strain-dependent measurements (Figure S9).Structural relaxation was found to occur on longer time scalesin the order Mg2+ < Zn2+ < Co2+ < Ni2+, corresponding to theincreasing strength of the coordination bonds. The obtainedrelaxation curves were fitted with a conventional single-exponential function, G(t) = G0 exp(−t/τ), from which theFigure 5. (a) Stress relaxation curves of 5 wt % TetraPEG ion gels(M2+ = Ni2+, Co2+, Zn2+, and Mg2+) at cM = 7.6 mM (cM/ctpy = 0.5).The Ni2+ data represent a time−temperature superposition mastercurve constructed from measurements at 293, 323, and 353 K(referenced to 293 K), whereas the Co2+, Zn2+, and Mg2+ data wereobtained at 293 K. Solid lines represent the fitting results using asingle-exponential relaxation model, G(t) = G0 exp(−t/τ). (b)Correlation between the relaxation time (log τ) and the bindingenergy (ΔEbind) of the M(tpy)22+ complexes obtained from DFTcalculations.Chemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c00832Chem. Mater. 2026, 38, 5723−57315728https://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c00832/suppl_file/cm6c00832_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832?fig=fig5&ref=pdfpubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c00832?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asrelaxation time (τ) was determined. The resulting τ valueswere 4.0 s for Mg2+, 6.5 s for Zn2+, 3.9 × 103 s for Co2+, and 1.2× 106 s for Ni2+, respectively. Figure 5b shows theexperimentally determined τ plotted against the bindingenergies (ΔEbind, shown as absolute values) of the M(tpy)22+complexes obtained from DFT calculations. The optimizedlowest-energy structures of the M−tpy complexes are providedin Figure S10. The plot shows a qualitative positive correlation,indicating that stronger M−tpy coordination interactions leadto longer relaxation times. This result suggests that thestructural relaxation of the MPF ion gels is closely related tothe strength of the interchain bridges formed by the M(tpy)22+complexes. Accordingly, the nature of the metal−ligandcoordination not only governs the static elasticity but alsoinfluences the dynamic mechanical response. These findingssuggest that the mechanical properties of MPF ion gels can betuned through appropriate selection of the metal ions andligand combinations.■ CONCLUSIONSIn summary, this study provides a quantitative molecular-levelframework linking coordination chemistry with polymerscience, thereby enabling rational control of the macroscopicelasticity of coordination-bonded MPF ion gels. Theequilibrium-based analysis revealed that the elastic modulusof the MPF ion gels is dominated by the concentration of bis-terpyridine complexes (M(tpy)22+) acting as network-forminginterchain bridges. In contrast, the dynamic viscoelasticity iscorrelated with the strength of the metal−ligand coordinationinteractions. These results clarify how molecular equilibriumdetermines the static elasticity and suggest that metal−ligandcoordination interactions also play an important role in thedynamic mechanical response of soft materials, providing a linkbetween molecular-level coordination interactions and macro-scopic mechanical properties.In particular, both the nonmonotonic dependence of G′ oncM and its variation across different metal ions (Mg2+ < Zn2+ <Co2+ < Ni2+) can be consistently explained by the attainableconcentration of the bis-terpyridine complex. The equilibriumconstants determined for these systems were higher than thosereported in aqueous solutions, indicating a pronounced shift incoordination equilibria in the IL environment. Furthermore,the stress relaxation behavior shows a correlation with thebinding energy of the coordination bonds, providing aconsistent relationship between coordination strength andrelaxation dynamics. These results provide a basis forunderstanding how coordination thermodynamics and inter-actions influence macroscopic mechanical properties in thisclass of materials. While further extension to a broader range ofmetal ions, ligand motifs, and polymer architectures will benecessary to establish general applicability, the present findingssuggest that coordination chemistry offers a viable strategy fortuning the elasticity and dynamics of polymer networks withinthe scope examined in this study.■ ASSOCIATED CONTENTData Availability StatementA preliminary version of this work has been deposited as apreprint on ChemRxiv.54*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c00832.Experimental and analysis; 1H NMR spectrum (FigureS1); G′ and G″ as a function of reaction time (FigureS2); SAXS profiles (Figure S3); G′ and G″ as a functionof frequency (Figure S4); photograph of TetraPEG-tpygelation using Li+ (Figure S5); G′ of chemically cross-linked ion gel (Figure S6); time-dependent UV−visspectra (Figure S7); concentrations of each metalspecies vs cM (Figure S8); strain-dependent measure-ments (Figure S9); optimized geometries of M2+−tpycomplexes (Figure S10); fitting parameters obtainedfrom SAXS (Table S1); equilibrium constants (TableS2) (PDF)■ AUTHOR INFORMATIONCorresponding AuthorsKenta Fujii − Graduate School of Sciences and Technology forInnovation, Yamaguchi University, Ube, Yamaguchi 755-8611, Japan; orcid.org/0000-0003-0057-1295;Email: k-fujii@yamaguchi-u.ac.jpTakeshi Ueki − Research Center for Macromolecules andBiomaterials, National Institute for Materials Science,Tsukuba, Ibaraki 305-0044, Japan; Graduate School of LifeScience, Hokkaido University, Sapporo, Hokkaido 060-0810,Japan; orcid.org/0000-0001-9317-6280;Email: UEKI.Takeshi@nims.go.jpAuthorsYoshika Kimura − Graduate School of Sciences andTechnology for Innovation, Yamaguchi University, Ube,Yamaguchi 755-8611, JapanAsuka Murao − Graduate School of Sciences and Technologyfor Innovation, Yamaguchi University, Ube, Yamaguchi 755-8611, JapanTomoya Tashiro − Graduate School of Sciences andTechnology for Innovation, Yamaguchi University, Ube,Yamaguchi 755-8611, JapanNoboru Osaka − Department of Chemistry, Faculty of Science,Okayama University of Science, Okayama 700-0005, JapanYuji Kamiyama − Research Center for Macromolecules andBiomaterials, National Institute for Materials Science,Tsukuba, Ibaraki 305-0044, JapanComplete contact information is available at:https://pubs.acs.org/10.1021/acs.chemmater.6c00832Author Contributions#Y.K. and A.M. contributed equally to this work (co-firstauthor).NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSThis work was financially supported by JSPS KAKENHI[Grant Numbers, JP23H02066 (K.F.), JP23K26759 (K.F.),JP22H00340 (K.F.), JP23H02030 (T.U.), and JP23K26723(T.U.)].■ REFERENCES(1) Rubinstein, M.; Colby, R. 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