Poly(ethylene oxide) (PEO)-based polymer electrolytes often exhibit coordination-coupled slowdown of ion and segmental dynamics, yet a compact descriptor for comparing the resulting dynamical constraints across salt concentrations remains lacking. In this work, united-atom molecular dynamics simulations are combined with a Sticky Rouse model (SRM) mapping to parameterize Li+–ether oxygen (EO) coordination-related slowdown in PEO-based single-ion-conducting polymer electrolytes. By introducing EO-neutralized tracer chains, we obtain a finite-time, tracer-referenced, chain-level apparent parameter, , that provides a physics-informed reduced-order measure of the apparent dynamical penalty per active Li+-coordinated EO site relative to the composition-dependent matrix background. Its scope is trend-level rather than that of a fully converged microscopic or Li+-specific transport-friction coefficient. The resulting increases monotonically with salt concentration. Its empirical exponential-like dependence is used as a phenomenological representation of nonlinear coordination-related slowdown and is qualitatively consistent with reported experimental trends. Microscopic analyses show that increasing is correlated with reduced apparent diffusivities, longer Li+–EO coordination lifetimes, reduced EO availability, less favorable multichain solvation, enhanced Li+–TFSI− association, and a redistribution of post-dissociation pathways among dissociation, re-coordination and hopping. These local changes are accompanied by stronger ionic clustering and a reorganization of dynamic heterogeneity at higher salt concentrations, highlighting the mean-field and trend-level scope of the SRM mapping. Because several systems remain subdiffusive within the accessible simulation window, the transport quantities discussed here are interpreted primarily at the trend level. Within this scope, the present work establishes a tracer-assisted SRM parameterization of coordination-related excess drag under composition-dependent matrix slowdown, supporting as an effective descriptor for comparing salt-concentration-dependent transport slowdown.

Associative polymers (APs) with star architectures offer a promising route to tailor the dynamics and mechanical properties of reversible polymer networks. However, establishing a predictive link between molecular topology and macroscopic viscoelasticity remains challenging. Here, we investigate the linear viscoelasticity (LVE) of unentangled associative star polymers by integrating the modified sticky Rouse model (SRM) and coarse-grained molecular simulations. By explicitly incorporating branched architectures into the SRM framework using graph theory, we derive analytical solutions for the LVE of star-shaped APs. To validate this approach and isolate the intrinsic topological contributions, we simulate well-defined vitrimer-like networks formed by unentangled telechelic star precursors using a hybrid Monte Carlo/molecular dynamics (hybrid MC/MD) algorithm. The simulation results exhibit quantitative agreement with theoretical predictions for stress relaxation and dynamic moduli, particularly in the terminal relaxation regime. We further reveal that star topology critically regulates terminal relaxation by modulating the local sticker encounter probability p sc, which determines the bond lifetime tau b through the prefactor tau b 0 similar to 1 p sc . Specifically, increasing the arm length significantly reduces the local sticker density, thereby suppressing sticker encounters and dramatically retarding terminal relaxation, whereas increasing the arm number at fixed arm length has a much weaker effect. A universal scaling between the relative friction coefficient delta and terminal relaxation time tau s (delta similar to tau s) is observed across all investigated networks. These results show that branched architectures geometrically suppress sticker encounters and thereby decouple association-controlled terminal relaxation from internal strand motion, without changing the intrinsic exchange barrier prescribed in the model. Our work extends the universality of the SRM to topological APs, providing molecular-level guidelines for designing materials with tailored viscoelastic functions.

The distinctive rheological behavior of associative polymers (APs) is commonly attributed to the supramolecular interactions between stickers, where transient bonds are continually forming and breaking. This ongoing disruption and reconstruction significantly extend the terminal relaxation time, endowing APs with properties similar to those of entangled polymers. Based on the fundamental sticky Rouse model (SRM), the terminal relaxation of APs can be understood as a result of a combination of strand motion and associative interactions. However, this explanation may be overly simplistic. The presence of multiple relaxation modes arising from a broader range of molecular processes introduces complexity, and their individual contributions to the terminal relaxation time remain uncertain. In this work, we focus on decoupling these multiple relaxation modes. Our findings reveal that, beyond strand motion and associative interactions, the terminal relaxation time is also influenced by factors such as the loss of cross-links, reassociation dynamics, and small molecule reactants. Furthermore, the difference between the activation energy required for strand motion and the magnitude of reaction kinetic activation energy between stickers plays a crucial role in determining the distribution of the terminal relaxation time. We believe that this work offers significant insights into the linear viscoelasticity (LVE) of APs.

We clarify the similarities and differences between Diss-CANs and Asso-CANs regarding their self-repairing capabilities, thus providing valuable insights for the efficient utilization of CANs in the development of self-repair materials.

Designing network topology with tunable dynamics and rheology behaviors is the key for vitrimers applications. In this study, PET vitrimers with varying crosslinking density and network homogeneity were created by using different Mw of precursors and branching agents (catalysts). Our results show that the dynamic network formed by propane-type branching agent such as 1,3-bis[tris(hydroxymethyl) methylamino] propane (BIS-TRIS propane), is more uniform due to steric hindrance effect compared to 2,2-Bis(hydroxymethyl)-2,2′,2″-nitrilotriethanol (BIS-TRIS). The thermal behavior of PET vitrimers was investigated by non-isothermal experiments, including glass transition and crystallization process. In particular, rheology behavior is sensitive to network structure and bond exchange process. The linear viscoelasticity (LVE) region of PET vitrimers is characterized by constructed pseudo-master curves that are guided by two distinct relaxation mechanisms: Rouse-type relaxation of strands and terminal relaxation of the network. Each relaxation mechanism is associated with a unique activation energy. The mechanical and processing properties of the PET vitrimers are reflected in their plateau modulus and characteristic relaxation time, which varies depending on the network topology. Based on the LVE analysis, we further investigated nonlinear rheology of PET vitrimers under extensional flow. Our results indicate that PET vitrimers exhibit significant strain hardening behavior, but display distinct stretching trends, corresponding to polymer melts' ductility. The ductility of materials decreases with a decrease in precursor's molecular weight (Mw), but improved with enhanced network homogeneity. Therefore, the crosslinking density and network homogeneity of dynamic network can be selectively tailored using appropriate precursors and branching agents to meet various industrial applications.

Covalently grafting polymer chains onto inorganic nanoparticles (NPs) with a sufficiently high grafting density (i.e. polymer brushes) is an effective way to combine the desired properties of core NPs (e.g. optical, electrical, and magnetic properties) with those of polymers (e.g. flexibility, processability, and environmental responsiveness). Binary mixed homopolymer brush-grafted NPs (MBNPs) refer to those grafted randomly or alternately with two types of chemically dissimilar homopolymer chains. They are not only "multifaceted" (i.e. incorporated with multiple functionalities) but also "smart" (i.e. stimuli-responsive). As predicted by theoretical studies and computer simulations, MBNPs can exhibit a variety of intriguing self-assembled morphologies, leading to a unique class of "patchy" NPs with a well-controlled distribution of two polymers on the NP surface. These nanostructures in turn will influence the hierarchical self-assembly of MBNPs into metamaterials at a larger length scale. In this book chapter, we review our recent progress in the study of self-assembly of the well-defined MBNPs prepared by a two-step surface-initiated reversible deactivation radical polymerization method from asymmetric difunctional initiator-functionalized silica particles. When the silica core NPs are larger than the polymer chain dimensions, the situation is reminiscent of mixed brushes grafted on a flat substrate. When the silica NP sizes are similar to the polymer chain dimensions, many ordered nanostructures can be obtained. In addition to the self-assembled nanostructures of MBNPs from solvent casting, their self-assembly in good and selective solvents and homopolymer matrices is also reviewed. Finally, future research direction is pointed out for the hierarchical self-assembly of MBNPs.

To enhance mechanical properties and processing performance of poly(ethylene terephthalate) (PET), it was upcycled to processable PET vitrimers with different crosslinking degrees by introducing dynamic network. The thermodynamics and linear viscoelasticity of PET vitrimers were explored by non-isothermal crystallization, isothermal sweep, frequency sweep and stress relaxation after incorporation of network. In particular, rheology experiments are sensitive to network structure and bond exchange mechanism in vitrimers. The pseudo-master curves show that relaxation processes are composed of three characteristic regions: Rouse-type relaxation of network strands, rubbery plateau and terminal relaxation of network, which is consistent with reversible gelation (RG) model. Two distinct (flow and chemical reaction) activation energies, are obtained by time-temperature superposition principle due to different temperature dependences of two relaxation behaviors. In addition, nonlinear rheology of PET vitrimers was investigated by extensional flow and start-up shear at the same Weissenberg number, and obvious strain hardening behavior were observed in all vitrimers. However, vitrimers with different crosslinking density exhibited distinct strain hardening trends as increase of extensional rate, corresponding to the ductility of material. On the basis of kinetics study, self-repairing and welding properties are further quantitatively explored for industrial applications.

Covalent adaptable networks (CANs) can be classified into dissociative (Diss-CANs) and associative (Asso-CANs) networks according to the exchange mechanism of covalent bonds. We simulate the exchange reaction by the discover the connection and difference between Diss-CANs and Asso-CANs in viscoelasticity behavior. In the linear regime, a major difference originating from the cross-linking density is reflected in the pre-exponential factor tau(s center dot) of the characteristic relaxation time tau s. For nonlinear rheology, Diss-CANs show a faster shear thinning behavior under steady shear, while Asso-CANs have a stronger strain hardening under the shear rate start-up. The physics behind the phenomenon results from the different chain conformations and configurations related to the exchange mechanism. Compared with Diss-CANs, the inability for sticker dissociation of Asso-CANs generates a slower relaxation under shear, leading to less chain orientation and tumbling. Meanwhile, we find that multiscale relaxation times obtained from linear viscoelasticity (LVE) can be crucial limits in nonlinear applications for associative polymers (APs). Our work strongly deepens the understanding of APs in terms of both linear and nonlinear viscoelasticities.

To improve the low crystallization rate and long molding cycle of Poly(ethylene terephthalate) (PET), series of PET nanocomposites incorporated small quantities of zeolites with different topologies were blended by melt compounding. The nucleation influence of 3-dimensional zeolites Y, ZSM-5 and 2-dimensional zeolite MCM-22P on the crystallization manner of PET was analyzed by non-isothermal and isothermal crystallization, quantitative evaluation of nanoparticle dispersion and morphology of nanoparticles. The results show that all PET/zeolite nanocomposites exhibit higher crystallization temperature and faster crystallization rate than PET due to large specificsurfacearea of zeolites and their superior dispersion in the PET matrix. Among them, PET/MCM-22P nanocomposites remarkably improved the crystallization behavior, thermal stability and oxygen barrier properties, which is related to the layered morphology of MCM-22P and hydrogen bond interactions between MCM-22P and PET. It is revealed that MCM-22P can provide more heterogeneous nucleation sites for PET by exfoliation in melting compounding. Furthermore, the nucleation mechanism induced by MCM-22P was investigated by the means of Mozhishen method, Avrami equation and theory of Hoffman-Lauritzen. The results indicate that the incorporation of MCM-22P can decrease the free energy of nucleation and fold surface in PET crystallization process, thus improving the crystallinity.

Dual polymer networks with stickers have a reputation for enhanced modulus and toughness. We propose a modified sticky Rouse model (SRM) from the single-chain perspective for permanent and transient dual networks, aiming to find a universal description of associative polymer dynamics. The computational complexity of obtaining the analytical relaxation spectrum is simplified by graph theory, implementing matrix reduction of the Rouse−Zimm matrix based on the symmetry. The analytical relaxation spectrum can also return to the case of linear polymers and permanent networks. The modified SRM for dual polymer networks predicts a Rouse-like scale of the linear relaxation modulus G(t) ∝ t−1/2 in sticker relaxation, consistent with the existing experimental results. In particular, the key parameter in the SRM, namely, the effective friction coefficient, can be extracted from the lifetime of sticky bonds and diffusion of chains, obtained by molecular dynamics simulations (MD). Based on that, the SRM model can predict the linear viscoelasticity of dual polymer networks, quantitatively in agreement with our MD results. Our work strongly supports the applicability of the singlechain molecular model SRM for polymer complex networks with reversible associative interactions.

Polyethylene terephthalate (PET) generally suffers from low crystallization rate and long molding cycle, which limits its application in injection molding of engineering plastics. To overcome the specific shortcoming, polymaleic acid-co-acrylic acid (PMA-AA) ionomer used as a nucleating agent was added to PET by melt blending, and its effect on the crystallization behavior of PET was investigated in this paper. It is indicated that the modified PET samples (MPET) with the addition of nucleating agents exhibit much higher molecular order and faster crystallization rate. The nucleation mechanism of MPET induced by PMA-AA ionomer was analyzed by means of Avrami equation and Hoffman–Lauritzen theory, revealing that the addition of PMA-AA ionomer provides more nucleation sites and reduces the fold surface free energy of PET. The nucleation and dispersion behavior of PMA-AA ionomer were further observed by SEM and POM morphologies. The results demonstrated that ionomer was dispersed homogeneously in the PET matrix, thus leading to faster crystallization rate of MPET than neat PET. In addition, the thermal stability, mechanical properties, and gas barrier of PET and MPET were characterized.

Polymers bearing associative groups (APs) are characterized by their fantastic viscoelastic behaviors. In a work recently published by our group [Jiang et al., Macromolecules 53, 3438–3451 (2020)], a single chain sticky Rouse model (SRM) is proposed to describe the linear viscoelasticity of APs without the entanglement effect. In this work, equilibrium molecular dynamics simulation of an unentangled melt of an AP with uniformly distributed stickers is carried out, and the dynamic properties are simultaneously analyzed from the SRM. A chain model with capped stickers is proposed so that a well-defined association chemistry is promised in the simulation system. The relative effective frictional coefficient of stickers, which is the key parameter in the SRM, is extracted from the chain center-of-mass diffusion, and it is found to be consistent with the dynamics of associative reaction in the fully gelated network. Based on this, a linear relaxation modulus and segmental diffusion functions are predicted from the SRM without fitting parameters, and these are found to quantitatively agree with the simulation results, showing the effectiveness of the SRM in connecting the dynamic properties at different molecular levels. The change in relaxation modes and the definition of the effective chain center are found to be crucial in the scenario of the SRM. Finally, the above analysis from the SRM is successfully extended to the simulation system with asymmetric chains. All these simulation results strongly support the SRM as a molecular model for the linear rheology of AP.

Anisotropic composite hydrogels have wide applications in the fields of materials for actuators and sen-sors.Herein,we report an anisotropic composite hydrogel prepared by a mechanical-strain-induced method.Polymer networks including poly(N-isopropylacrylamide)(PNIPAM)and sodium alginate(SA),as well as carbon nanotubes(CNTs)are found to align simultaneously by stretching,and then fixed by physical crosslinking through non-covalent bonds.Com-posite hydrogels with doubly aligned polymer networks showed anisotropic optical and mechanical properties.The actuation performance of the anisotropic composite hydrogels as compared with the isotropic ones was found to be enhanced,which showed the capability of lifting 100 times its weight with 20％contraction strain.Besides,a bilayer hydrogel was de-signed to bend with a maximum of 390° to mimic the tendril behavior of plants.

A hydrogel is a three-dimensional network of hydrophilic polymers, which can hold a large amount of water while maintaining the structure. Due to its "soft" and "wet" characteristics, the resemblance to living tissue opens up many opportunities for applications in biomedical areas. However, compared with soft tissues, traditional hydrogels have rather weak mechanical properties due to the uneven cross-linking structures during polymerizations. Also, the mechanical properties of the hydrogels are isotropic, as oppose to most of the soft tissues, which are always anisotropic. Many soft tissues in nature are composed of multi-level anisotropic structures, which give animals the abilities to adapt changes in the harsh environment. Inspired by the anisotropic structure in nature, how to introduce highly ordered structures into hydrogel networks has become a hot research topic in recent years. Among the thermos.responsive polymers, poly (N-isopropylacrylamide) (PNIPAM) is the most important one because of transition across the lower critical solubility temperature (LCST). This unique property endows PNIPAM the ability to be used as smart actuators. In this review, several strategies of fabricating anisotropic PNIPAM. based smart actuators are summarized, and the impact of anisotropic structures on their actuating abilities are discussed in detail.

It is known that the nucleation of liquid crystal polymers with orientation interactions can reduce the energy barrier during the polymer crystallization. In this work, we combine the SCFT and string method to explore the nucleation and liquid crystal behavior of rod-coil block copolymers. By examining nucleation transitions from cylinders with different directions to lamellae, we obtain the information of critical nuclei for the first time, including the volume, shape and energy barrier. We further investigate the impacts of orientation interactions along different transition paths. The results show that if the cylinder and lamellae have inconsistent directions, the nucleation will occur with relatively longer transition path and multiple reorientations, and thus leading to higher energy barrier. Nucleation under different Flory-Huggins interactions and nucleation via precursory metastable structures are investigated, and compared with the classical nucleation theory. This work develops the nucleation studies for complex block copolymers with segment orientations, which is helpful for understanding the nucleation of liquid crystal polymers.

Polymers bearing associative groups can exhibit fascinating rheological behaviors. A modified version of the Rouse model, which is originally used in block copolymers and called the sticky Rouse model here, is proposed to describe the linear viscoelasticity (LVE) of this kind of polymers without the effect of entanglement. By replacing the lifetime of a transient bond by the effective friction on stickers, the calculation of LVE functions is turned into the eigenvalue problem of the sticky Rouse-Zimm (RZ) matrix. The results show that only two parameters, sticker concentration representing the network microstructure and association interaction strength, can understand the LVE for associative polymers. In particular, the description of LVE from previous theories can be integrated in this unified theoretical framework. From the analysis of eigenvectors, it is further inferred that the rotational motion of bridge structures should be responsible for the longest relaxation times in rheology.

On the basis of self-consistent field theory (SCFT), we demonstrate that X-shaped rod–coil molecules with hydrogen-bonding groups self-assemble into Archimedean tiling patterns including [36], [44], [63], [3.4.6.4], and [(3.6)2], and dual tiling patterns including dual-[32.4.3.4]. The rod blocks form the edges of polygons, coil blocks fill in the inner spaces of polygons, and the existence of hydrogen bonds further decreases the domain size. A new mechanism is proposed to guide the formation of Archimedean tiling patterns: the fabrication of tiling patterns is controlled by the relationship between the length–diameter ratio β and volume fraction fR of rigid cores in X-shaped supra-macromolecules. This study provides a concept of macromolecular tiling for producing Archimedean tilings and suggests X-shaped rod–coil supra-macromolecules with hydrogen-bonding groups as an ideal platform for the fabrication of two-dimensional nanoscale patterns.

Polymer brushes have wide application in surface modification. We study dense, short polymer brushes immersed in a mixing solvent under athermal conditions using the classical density functional theory. The brush polymer is short so that the equilibrium behavior of the brush deviates far from the scaling laws for infinite brush chains. The excluded volume interaction is the only interaction in the system. We compare the excluded volume effect of solvent molecules of different shapes. Two types of mixing solvents are considered: solvent composed of linear oligomers and monomers, or that of spherical particles and monomers. The effects of grafting density, solvent molecular size, and solvent number density on the brush height, the density profiles, the relative excess adsorption, and the brush-solvent interface width are systematically analyzed. In the adsorption aspect, the spherical particles have stronger ability than the linear oligomers do to penetrate through the brush layer and gather at the substrate. In the screening aspect, the oligomers are more capable of screening the excluded volume interaction between the brush chains than the spherical particles. The brush-solvent interface width decreases monotonically with increasing oligomer length, but it has a minimum with the increasing spherical particle size. Our research differentiates the attractive-interaction-induced phenomenon and the volume-exclusion-induced phenomenon in dense brush systems and exhibits the difference in the antifouling properties of the brushes contacting solvent molecules of different shapes.

We apply the string method to the self-consistent mean-field theory framework of the rod-coil block copolymer system to calculate the minimum energy pathways in the rearrangement transitions of lamellae and cylinders with different orientations under certain epitaxial growth relationship. Metastable phases appearing in the reordering transition pathway tend to form the structure at low χN side of the order-order transition boundary compared with the initial phase. In particular, for complex network, metastable phases, such as single gyroid and perforated lamellae, need to select a rearrangement transition between lamellae or cylinders near the order-disorder transition boundary with the same epitaxial growth relationship but different orientations. It is confirmed that this strategy for obtaining complex metastable phases by rational design of rearrangement transition between specific phases in the phase diagram can be applied to a wide range of χN as well as the coil-coil block copolymer system. We further investigate the rearrangement transition behavior combining with the analysis of contribution from the free energy, entropy, degree of mixing between different blocks, and the average orientation degree of rods during the phase transitions. Based on this mechanism, we have developed a target-directed design strategy for constructing self-assembled metastable structures of rod-coil block copolymers.