Topological Structure of Networks Formed from Symmetric Four-Arm Precursors

Topological linking determines elasticity in limited valence networks

Understanding the relationship between the microscopic structure and topology of a material and its macroscopic properties is a fundamental challenge across a wide range of systems. Here we investigate the viscoelasticity of DNA nanostar hydrogels-a model system for physical networks with limited valence-by coupling rheology measurements, confocal imaging and molecular dynamics simulations. We discover that these networks display a large degree of interpenetration and that loops within the network are topologically linked, forming a percolating network-within-network structure. Below the overlapping concentration, the fraction of branching points and the pore size determine the high-frequency elasticity of these physical gels. At higher concentrations, we discover that this elastic response is dictated by the abundance of topological links between looped motifs in the gel. Our findings highlight the emergence of 'topological elasticity' as a previously overlooked mechanism in generic network-forming liquids and gels and inform the design of topologically controllable material behaviours.

Photochemical Control of Network Topology in PEG Hydrogels

Hydrogels are often synthesized through photoinitiated step-, chain-, and mixed-mode polymerizations, generating diverse network topologies and resultant material properties that depend on the underlying network connectivity. While many photocrosslinking reactions are available, few afford controllable connectivity of the hydrogel network. Herein, a versatile photochemical strategy is introduced for tuning the structure of poly(ethylene glycol) (PEG) hydrogels using macromolecular monomers functionalized with maleimide and styrene moieties. Hydrogels are prepared along a gradient of topologies by varying the ratio of step-growth (maleimide dimerization) to chain-growth (maleimide-styrene alternating copolymerization) network-forming reactions. The initial PEG content and final network physical properties (e.g., modulus, swelling, diffusivity) are tailored in an independent manner, highlighting configurable gel mechanics and reactivity. These photochemical reactions allow high-fidelity photopatterning and 3D printing and are compatible with 2D and 3D cell culture. Ultimately, this photopolymer chemistry allows facile control over network connectivity to achieve adjustable material properties for broad applications.

Reversible two-way tuning of thermal conductivity in an end-linked star-shaped thermoset

Polymeric thermal switches that can reversibly tune and significantly enhance their thermal conductivities are desirable for diverse applications in electronics, aerospace, automotives, and medicine; however, they are rarely achieved. Here, we report a polymer-based thermal switch consisting of an end-linked star-shaped thermoset with two independent thermal conductivity tuning mechanisms-strain and temperature modulation-that rapidly, reversibly, and cyclically modulate thermal conductivity. The end-linked star-shaped thermoset exhibits a strain-modulated thermal conductivity enhancement up to 11.5 at a fixed temperature of 60 °C (increasing from 0.15 to 2.1 W m-1 K-1). Additionally, it demonstrates a temperature-modulated thermal conductivity tuning ratio up to 2.3 at a fixed stretch of 2.5 (increasing from 0.17 to 0.39 W m-1 K-1). When combined, these two effects collectively enable the end-linked star-shaped thermoset to achieve a thermal conductivity tuning ratio up to 14.2. Moreover, the end-linked star-shaped thermoset demonstrates reversible tuning for over 1000 cycles. The reversible two-way tuning of thermal conductivity is attributed to the synergy of aligned amorphous chains, oriented crystalline domains, and increased crystallinity by elastically deforming the end-linked star-shaped thermoset.

Tailoring Network Topology in Mechanically Robust Hydrogels for 3D Printing and Injection

Tissue engineering and regenerative medicine are confronted with a persistent challenge: the urgent demand for robust, load-bearing, and biocompatible scaffolds that can effectively endure substantial deformation. Given that inadequate mechanical performance is typically rooted in structural deficiencies─specifically, the absence of energy dissipation mechanisms and network uniformity─a crucial step toward solving this problem is generating synthetic approaches that enable exquisite control over network architecture. This work systematically explores structure-property relationships in poly(ethylene glycol)-based hydrogels constructed utilizing thiol-yne chemistry. We systematically vary polymer concentration, constituent molar mass, and cross-linking protocols to understand the impact of architecture on hydrogel mechanical properties. The network architecture was resolved within the molecular model of Rubinstein-Panyukov to obtain the densities of chemical cross-links and entanglements. We employed both nucleophilic and radical pathways, uncovering notable differences in mechanical response, which highlight a remarkable degree of versatility achievable by tuning readily accessible parameters. Our approach yielded hydrogels with good cell viability and remarkably robust tensile and compression profiles. Finally, the hydrogels are shown to be amenable to advanced processing techniques by demonstrating injection- and extrusion-based 3D printing. Tuning the mechanism and network regularity during the cell-compatible formation of hydrogels is an emerging strategy to control the properties and processability of hydrogel biomaterials by making simple and rational design choices.

Disulfide-Cross-Linked Tetra-PEG Gels

The preparation of polymer gels via cross-linking of four-arm star-shaped poly(ethylene glycol) (Tetra-PEG) precursors is an attractive strategy to prepare networks with relatively well-defined topologies. Typically, Tetra-PEG gels are obtained by cross-linking heterocomplementary reactive Tetra-PEG precursors. This study, in contrast, explores the cross-linking of self-reactive, thiol-end functional Tetra-PEG macromers to form disulfide-cross-linked gels. The structure of the disulfide-cross-linked Tetra-PEG gels was studied with multiple-quantum NMR (MQ-NMR) spectroscopy and small-angle neutron scattering (SANS) experiments. In line with earlier simulation studies, these experiments showed a strong dependence of the relative fractions of the different network connectivities on the concentration of the thiol-end functional Tetra-PEG macromer that was used for the synthesis of the networks. Disulfide-cross-linked Tetra-PEG gels prepared at macromer concentrations below the overlap concentration (c = 0.66c*) primarily feature defect connectivity motifs, such as primary loops and dangling ends. For networks prepared at macromer concentrations above the overlap concentration, the fraction of single-link connectivities was found to be similar to that in amide-cross-linked Tetra-PEG gels obtained by heterocomplementary cross-linking of N-hydroxysuccinimide ester and amine functional Tetra-PEG macromers. Since disulfide bonds are susceptible to reductive cleavage, these disulfide-cross-linked gels are of interest, e.g., as reduction-sensitive hydrogels for a variety of biomedical applications.

Confinement effect of inter-arm interactions on glass formation in star polymer melts

We utilized molecular dynamic simulation to investigate the glass formation of star polymer melts in which the topological complexity is varied by altering the number of star arms (f). Emphasis was placed on how the "confinement effect" of repulsive inter-arm interactions within star polymers influences the thermodynamics and dynamics of star polymer melts. All the characteristic temperatures of glass formation were found to progressively increase with increasing f, but unexpectedly the fragility parameter KVFT was found to decrease with increasing f. As previously observed, stars having more than 5 or 6 arms adopt an average particle-like structure that is more contracted relative to the linear polymer size having the same mass and exhibit a strong tendency for intermolecular and intramolecular segregation. We systematically analyzed how varying f alters collective particle motion, dynamic heterogeneity, the decoupling exponent ζ phenomenologically linking the slow β- and α-relaxation times, and the thermodynamic scaling index γt. Consistent with our hypothesis that the segmental dynamics of many-arm star melts and thin supported polymer films should exhibit similar trends arising from the common feature of high local segmental confinement, we found that ζ increases considerably with increasing f, as found in supported polymer films with decreasing thickness. Furthermore, increasing f led to greatly enhanced elastic heterogeneity, and this phenomenon correlates strongly with changes in ζ and γt. Our observations should be helpful in building a more rational theoretical framework for understanding how molecular topology and geometrical confinement influence the dynamics of glass-forming materials more broadly.

Structural Homogeneity of Macromolecular Networks by End-to-End Click Chemistry between Discrete Tetrahedral Star Macromolecules

Cross-linking via the end-to-end click chemistry of multiarm star polymers creates polymer networks with minimal inhomogeneities. Although it has been suggested that the mechanical and swelling properties of such networks depend on the absence of defects, the structural details of homogeneous networks created by this method have not yet been studied at the molecular level. Here, we report the synthesis of discrete tetrahedral star macromolecules (dTSMs) composed of polylactide (PLA) arms with discrete molecular weight and sequence. Polymer networks prepared by 4 × 4 cross-linking by Cu-free strain-promoted cyclooctyne-azide click chemistry (SPAAC) reaction exhibited a high degree of swelling (>40 fold by weight) in solvents without sacrificing mechanical robustness (elastic modulus >4 kPa). The structural details of the networks were investigated by network disassembly spectrometry (NDS) using MALDI-TOF mass spectrometry. By implementing a cleavable repeating unit in the discrete PLA arms of dTSM in a sequence-specific manner, the networks could be disassembled into fragments having discrete molecular weights precisely representing their connectivity in the network. This NDS analysis confirmed that end-to-end click reactions of dTSM networks resulted in the formation of a homogeneous network above the critical concentration (∼10 w/v%) of building blocks in the solution.

The network structure in transient telechelic polymer networks: extension of the Miller-Macosko model

The combination of supramolecular chemistry and polymer science has resulted in the development of transient polymer networks with diverse properties and applications. Specifically, polymer networks based on transient linking of telechelic polymer precursors offer a high degree of control over the network structure, which can reform in response to external stimuli that change the connectivity of transient bonds. Therefore, the combination of the versatile polymer functionality and the adjustable connectivity of transient bonds may result in complex network structures that are not easy to predict or characterize. To address this gap, herein we extend the Miller-Macosko model to forecast the network connectivity of transient telechelic polymer networks made with various polymer functionalities and transient connectivities represented by metal-ligand complexes. This model predicts a universal dependence of the network structure and modulus on preparative parameters including the metal ion identity, characterized by the complexation thermodynamics, and concentration. Moreover, we demonstrate that given the thermodynamic tendency of forming network defects like loops, the model can include such imperfections, enabling rheological properties to be used indirectly for the characterization of defect content. We outline general guidelines to extend the model to more intricate structures, enhancing our understanding of the structure-property relationship in complex transient polymer networks.

Shear Thickening Behavior in Injectable Tetra-PEG Hydrogels Cross-Linked via Dynamic Thia-Michael Addition Bonds

Injectable poly(ethylene glycol) (PEG)-based hydrogels were reversibly cross-linked through thia-conjugate addition bonds and demonstrated to shear thicken at low shear rates. Cross-linking bond exchange kinetics and dilute polymer concentrations were leveraged to tune hydrogel plateau moduli (from 60 to 650 Pa) and relaxation times (from 2 to 8 s). Under continuous flow shear rheometry, these properties affected the onset of shear thickening and the degree of shear thickening achieved before a flow instability occurred. The changes in viscosity were reversible whether the shear rate increased or decreased, suggesting that chain stretching drives this behavior. Given the relevance of dynamic PEG hydrogels under shear to biomedical applications, their injectability was investigated. Injection forces were found to increase with higher polymer concentrations and slower bond exchange kinetics. Altogether, these results characterize the nonlinear rheology of dilute, dynamic covalent tetra-PEG hydrogels and offer insight into the mechanism driving their shear thickening behavior.

Influence of solvent quality on the swelling and deswelling and the shear modulus of semi-dilute solution cross-linked poly(vinyl acetate) gels

We systematically examine the influence of varying temperature (T) over a large range in model poly(vinyl acetate) gels swollen in isopropyl alcohol. The theta temperature Θ, at which the second virial coefficient A2 vanishes, is found to be equal to within numerical uncertainty to the corresponding high molecular mass polymer solution value without cross-links, and we quantify the swelling and deswelling of our model gels relative to their size at T = Θ, as customary for individual flexible polymer chains in solutions. We also quantify the "solvent quality" dependence of the shear modulus G relative to G(T = Θ) and compare to the hydrogel swelling factor, α. We find that all our network swelling and deswelling data can be reduced to a scaling equation of the same general form as derived from renormalization group theory for flexible linear polymer chains in solutions so that it is not necessary to invoke either the Flory-Huggins mean field theory or the Flory-Rehner hypothesis that the elastic and mixing contributions to the free energy of network swelling are separable to describe our data. We also find that changes of G relative to G(T = Θ) are directly related to α. At the same time, we find that classical rubber elasticity theory describes many aspects of these semi-dilute solution cross-linked networks, regardless of the solvent quality, although the prefactor clearly reflects the existence of network defects whose concentration depends on the initial polymer concentration of the polymer solution from which the networks were synthesized.

Gelation Dynamics during Photo-Cross-Linking of Polymer Nanocomposite Hydrogels

Embedding nanomaterials into polymer hydrogels enables the design of functional materials with tailored chemical, mechanical, and optical properties. Nanocapsules that protect interior cargo and disperse readily through a polymeric matrix have drawn particular interest for their ability to integrate chemically incompatible systems and to further expand the parameter space for polymer nanocomposite hydrogels. The properties of polymer nanocomposite hydrogels depend on the material composition and processing route, which were explored systematically in this work. The gelation kinetics of network-forming polymer solutions with and without silica-coated nanocapsules bearing polyethylene glycol (PEG) surface ligands were investigated using in situ dynamic rheology measurements. Network-forming polymers comprised either 4-arm or 8-arm star PEG with terminal anthracene groups, which dimerize upon irradiation with ultraviolet (UV) light. The PEG-anthracene solutions exhibited rapid gel formation upon UV exposure (365 nm); gel formation was observed as a crossover from liquid-like to solid-like behavior during in situ small-amplitude oscillatory shear rheology. This crossover time was non-monotonic with polymer concentration. Far below the overlap concentration (c/c* ≪ 1), spatially separated PEG-anthracene molecules were subject to forming intramolecular loops over intermolecular cross-links, thereby slowing the gelation process. Near the polymer overlap concentration (c/c* ∼ 1), rapid gelation was attributed to the ideal proximity of anthracene end groups from neighboring polymer molecules. Above the overlap concentration (c/c* > 1), increased solution viscosities hindered molecular diffusion, thereby reducing the frequency of dimerization reactions. Adding nanocapsules to PEG-anthracene solutions resulted in faster gelation than nanocapsule-free PEG-anthracene solutions with equivalent effective polymer concentrations. The final elastic modulus of nanocomposite hydrogels increased with nanocapsule volume fraction, signifying synergistic mechanical reinforcement by nanocapsules despite not being cross-linked into the polymer network. Overall, these findings quantify the impact of nanocapsule addition on the gelation kinetics and mechanical properties of polymer nanocomposite hydrogels, which are promising materials for applications in optoelectronics, biotechnology, and additive manufacturing.

Non-Covalently Associated Streptavidin Multi-Arm Nanohubs Exhibit Mechanical and Thermal Stability in Cross-Linked Protein-Network Materials

Constructing protein-network materials that exhibit physicochemical and mechanical properties of individual protein constituents requires molecular cross-linkers with specificity and stability. A well-known example involves specific chemical fusion of a four-arm polyethylene glycol (tetra-PEG) to desired proteins with secondary cross-linkers. However, it is necessary to investigate tetra-PEG-like biomolecular cross-linkers that are genetically fused to the proteins, simplifying synthesis by removing additional conjugation and purification steps. Non-covalently, self-associating, streptavidin homotetramer is a viable, biomolecular alternative to tetra-PEG. Here, a multi-arm streptavidin design is characterized as a protein-network material platform using various secondary, biomolecular cross-linkers, such as high-affinity physical (i.e., non-covalent), transient physical, spontaneous chemical (i.e., covalent), or stimuli-induced chemical cross-linkers. Stimuli-induced, chemical cross-linkers fused to multi-arm streptavidin nanohubs provide sufficient diffusion prior to initiating permanent covalent bonds, allowing proper characterization of streptavidin nanohubs. Surprisingly, non-covalently associated streptavidin nanohubs exhibit extreme stability, which translates into material properties that resemble hydrogels formed by chemical bonds even at high temperatures. Therefore, this study not only establishes that the streptavidin nanohub is an ideal multi-arm biopolymer precursor but also provides valuable guidance for designing self-assembling nanostructured molecular networks that can properly harness the extraordinary properties of protein-based building blocks.

Brownian simulations for tetra-gel-type phantom networks composed of prepolymers with bidisperse arm length

We studied the effect of arm length contrast of prepolymers on the mechanical properties of tetra-branched networks via Brownian dynamics simulations. We employed a bead-spring model without the excluded volume interactions, and we did not consider the solvent explicitly. Each examined 4-arm star branch prepolymer has uneven arm lengths to attain two-against-two (2a2) or one-against-three (1a3) configurations. The arm length contrast was varied from 38-2 to 20-20 for 2a2, and from 5-25 to 65-5 for 1a3, with the fixed total bead number of 81, including the single bead located at the branch point for prepolymers. We distributed 400 molecules in the simulation box with periodic boundary conditions, and the bead number density was fixed at 4. We created polymer networks by cross-end-coupling of equilibrated tetra-branched prepolymers. To mimic the experiments of tetra gels, we discriminated the molecules into two types and allowed the reaction only between different types of molecules at their end beads. The final conversion ratio was more than 99%, at which unreacted dangling ends are negligible. We found that the fraction of double linkage, in which two of the four arms connect a pair of branch points, increases from 3% to 15% by increasing the arm length contrast. We stretched the resultant tetra-type networks to obtain the ratio of mechanically effective strands. We found that the ratio is 96% for the monodisperse system, decreasing to 90% for high arm length contrast. We introduced bond scission according to the bond stretching to observe the network fracture under sufficiently slow elongation. The fracture behavior was not correlated with the fraction of double linkage because the scission occurs at single linkages.

Molecular dynamics studies of entropic elasticity of condensed lattice networks connected with uniform functionality f = 4

To study the linear region of entropic elasticity, we considered the simplest physical model possible and extracted the linear entropic regime by using the least squares fit and the minimum of the mean absolute error. With regard to the effect of the fluctuation of the strand length N_s, the strand length with fluctuation was set to a form proportional to (1.0 + C (R - 0.5)), where R is a uniform random number between 0 and 1 and C is the amplitude of fluctuation. This form enabled us to analytically calculate the fluctuation dependence of the elastic modulus G. To reveal the linear regions of entropic elasticity as a function of the strand length between neighboring nodes in lattices, molecular dynamics (MD) simulations of condensed lattice networks with harmonic bonds without the excluded volume interactions were performed. Stress-strain curves were estimated by performing uniaxial stretching MD simulations under periodic boundary conditions with a bead number density of 0.85. First, we used a diamond lattice with functionality f = 4. The linear region of the entropic elasticity was found to become larger with the increasing number of beads in a strand N_s. For N_s = 100, the linear region had a strain of up to 8 for a regular diamond lattice. We investigated the effect of strand length fluctuation on the diamond lattice, and we confirmed that the equilibrium shear modulus G increases as the obtained analytical prediction and the linear entropic region in the stress-strain curves becomes narrower with increasing fluctuation of N_s. To investigate the difference in network topology with the same functionality f and uniform strand length N_s, we performed MD simulations on regular networks of the BC-8 structure with f = 4 prepared from the ab initio DFT calculations of carbon at high pressure. We found that the elastic behavior depends on the network connectivity (i.e., topology). This indicates that the network topology plays an important role in the emergence of nonlinearity owing to the crossover from entropic to energetic elasticity.

Structural aspects controlling the mechanical and biological properties of tough, double network hydrogels

Anticipating an increasing demand for hybrid double network (DN) hydrogels in biomedicine and biotechnology, this study evaluated the effects of each network on the mechanical and biological properties. Polyethylene glycol (PEG) (meth)acrylate hydrogels with varied monomer molecular weights and architectures (linear vs. 4-arm) were produced with and without an added ionically bonded alginate network and their mechanical properties were characterized using compression testing. The results showed that while some mechanical properties of PEG single network (SN) hydrogels decreased or changed negligibly with increasing molecular weight, the compressive modulus, strength, strain to failure, and toughness of DN hydrogels all significantly increased with increased PEG monomer molecular weight. At a fixed molecular weight (10 kDa), 4-arm PEG SN hydrogels exhibited better overall mechanical performance; however, this benefit was diminished for the corresponding DN hydrogels with comparable strength and toughness and lower strain to failure for the 4-arm case. Regardless of the PEG monomer structure, the alginate network made a relatively larger contribution to the overall DN mechanical properties when the covalent PEG network was looser with a larger mesh size (e.g., for larger monomer molecular weight and/or linear architecture) which presumably enabled more ionic crosslinking. Considering the biological performance, adipose derived stem cell cultures demonstrated monotonically increasing cell area and Yes-associated protein related mechanosensing with increasing amounts of alginate from 0 to 2 wt.%, demonstrating the possibility for using DN hydrogels in guiding musculoskeletal differentiation. These findings will be useful to design suitable hydrogels with controllable mechanical and biological properties for mechanically demanding applications. STATEMENT OF SIGNIFICANCE: Hydrogels are widely used in commercial applications, and recently developed hybrid double network hydrogels have enhanced strength and toughness that will enable further expansion into more mechanically demanding applications (e.g., medical implants, etc.). The significance of this work is that it uncovers some key principles regarding monomer molecular weight, architecture, and concentration for developing strong and tough hybrid double network hydrogels that would not be predicted from their single network counterparts or a linear combination of the two networks. Additionally, novel insight is given into the biological performance of hybrid double network hydrogels in the presence of adipose derived stem cell cultures which suggests new scope for using double network hydrogels in guiding musculoskeletal differentiation.

Star polymer networks: a toolbox for cross-linked polymers with controlled structure

The synthesis of precisely controlled polymer networks has been a long-cherished dream of polymer scientists. Traditional random cross-linking strategies often lead to uncontrolled networks with various kinds of defects. Recent...

Controlling Degradation and Erosion of Polymer Networks: Insights from Mesoscale Modeling

Understanding and controlling degradation of polymer networks on the mesoscale is critical for a range of applications. We utilize dissipative particle dynamics to capture photocontrolled degradation and erosion processes in hydrogels formed by end-linking of four-arm polyethylene glycol precursors. We demonstrate that the polydispersity and the fraction of broken-off fragments scale with the relative extent of reaction. The reverse gel point measured is close to the value predicted by the bond percolation theory on a diamond lattice. We characterize the erosion process via tracking the mass loss that accounts for the fragments remaining in contact with the percolated network. We quantify the dependence of the mass loss on the extent of reaction and on the properties of the film prior to degradation. These results elucidate the main features of degradation and erosion on the mesoscale and could provide guidelines for future design of degrading materials with dynamically controlled properties.

Adding the Effect of Topological Defects to the Flory-Rehner and Bray-Merrill Swelling Theories

The Flory-Rehner and Bray-Merrill swelling theories are venerable theories for calculating the swelling of polymer networks and are widely applied across polymer materials. Here, these theories are revised to include cyclic topological defects present in polymer networks by using a modified phantom network model. These closed-form equations assume defect contributions to the swelling elasticity to be linear and additive and allow different assumptions regarding prestrain of larger loops to be incorporated. To compare to the theories, swelling experiments are performed on end-linked poly(ethylene glycol) gels in which the topological defects (primary and secondary loops) have been previously measured. Gels with higher loop densities exhibit higher swelling ratios. An equation is derived to compare swelling models independent of knowledge of the Flory-Huggins χ parameter, showing that the revised swelling models for loop defects are more accurate than both the phantom network model that neglects loops and the Bray-Merrill equation.

Tailoring Crosslinked Polyether Networks for Separation of CO2 from Light Gases

Crosslinked poly(ethylene oxide) or poly(ethylene glycol) (PEG) is an ideal membrane material for separation of CO₂ from light gases (e.g., H₂ , N₂ , O₂ , CH₄ etc). In these membranes, crosslinking is used as a tool to suppress crystallinity of the PEG segments. In spite of the extensive effort to develop crosslinked PEG membranes in the last two decades, it remains a challenge to establish the structure-property relationships. This paper points out the fundamental limitations to correlate the chain topology of a network with the gas permeation mechanism. While a quantitative comparison of the molecular weight between crosslinks of networks and gas permeation mechanism reported by different research groups is challenging, effort is made to draw a qualitative picture. In this review, a focus is also put on the progress of utilization of dangling chain fractions to tailor the gas permeation behavior of PEG networks.

Molecular Characterization of Polymer Networks

Polymer networks are complex systems consisting of molecular components. Whereas the properties of the individual components are typically well understood by most chemists, translating that chemical insight into polymer networks themselves is limited by the statistical and poorly defined nature of network structures. As a result, it is challenging, if not currently impossible, to extrapolate from the molecular behavior of components to the full range of performance and properties of the entire polymer network. Polymer networks therefore present an unrealized, important, and interdisciplinary opportunity to exert molecular-level, chemical control on material macroscopic properties. A barrier to sophisticated molecular approaches to polymer networks is that the techniques for characterizing the molecular structure of networks are often unfamiliar to many scientists. Here, we present a critical overview of the current characterization techniques available to understand the relation between the molecular properties and the resulting performance and behavior of polymer networks, in the absence of added fillers. We highlight the methods available to characterize the chemistry and molecular-level properties of individual polymer strands and junctions, the gelation process by which strands form networks, the structure of the resulting network, and the dynamics and mechanics of the final material. The purpose is not to serve as a detailed manual for conducting these measurements but rather to unify the underlying principles, point out remaining challenges, and provide a concise overview by which chemists can plan characterization strategies that suit their research objectives. Because polymer networks cannot often be sufficiently characterized with a single method, strategic combinations of multiple techniques are typically required for their molecular characterization.

Heterogeneity Effects in Highly Cross-Linked Polymer Networks

Despite their level of refinement, micro-mechanical, stretch-based and invariant-based models, still fail to capture and describe all aspects of the mechanical properties of polymer networks for which they were developed. This is for an important part caused by the way the microscopic inhomogeneities are treated. The Elastic Network Model (ENM) approach of reintroducing the spatial resolution by considering the network at the level of its topological constraints, is able to predict the macroscopic properties of polymer networks up to the point of failure. We here demonstrate the ability of ENM to highlight the effects of topology and structure on the mechanical properties of polymer networks for which the heterogeneity is characterised by spatial and topological order parameters. We quantify the macro- and microscopic effects on forces and stress caused by introducing and increasing the heterogeneity of the network. We find that significant differences in the mechanical responses arise between networks with a similar topology but different spatial structure at the time of the reticulation, whereas the dispersion of the cross-link valency has a negligible impact.

Optimizing the heterogeneous network structure to achieve polymer nanocomposites with excellent mechanical properties

Designing and optimizing the polymer network structure at the molecular level to manipulate its mechanical properties are of great scientific significance. Although heterogeneous multi-network structures have been extensively investigated, little effort has been devoted to investigating heterogeneous single-networks with a well-defined interface. Herein, through coarse-grained molecular dynamics simulation, we successfully fabricated a heterogeneous single-network, which was divided into several regions with different crosslink densities. Firstly, we found that there is an optimal crosslink density ratio between high and low crosslink density regions to obtain the best stress-strain behavior. Secondly, the effect of the regularity of the network topology (by changing the distribution of two-phase regions) on mechanical properties was also studied. It was clearly observed that the polymer network showed better elastic response and mechanical properties as the distribution of two-phase regions became uniform. Finally, we investigated the effect of the selective distribution of nanoparticles (NPs) on mechanical properties by introducing NPs into a pre-designed multiphase network. Results showed that the selective distribution of NPs in the high crosslink density region had a more significant effect on the mechanical reinforcement. Generally, our simulated results may provide some guidelines to design polymer network structures to achieve high-performance polymer nanocomposites with excellent mechanical properties.

Defects and defect engineering in Soft Matter

Soft matter covers a wide range of materials based on linear or branched polymers, gels and rubbers, amphiphilic (macro)molecules, colloids, and self-assembled structures. These materials have applications in various industries, all highly important for our daily life, and they control all biological functions; therefore, controlling and tailoring their properties is crucial. One way to approach this target is defect engineering, which aims to control defects in the material's structure, and/or to purposely add defects into it to trigger specific functions. While this approach has been a striking success story in crystalline inorganic hard matter, both for mechanical and electronic properties, and has also been applied to organic hard materials, defect engineering is rarely used in soft matter design. In this review, we present a survey on investigations on defects and/or defect engineering in nine classes of soft matter composed of liquid crystals, colloids, linear polymers with moderate degree of branching, hyperbranched polymers and dendrimers, conjugated polymers, polymeric networks, self-assembled amphiphiles and proteins, block copolymers and supramolecular polymers. This overview proposes a promising role of this approach for tuning the properties of soft matter.

Fracture of polymer networks with diverse topological defects

Polymer networks are pervasive in biological organisms and engineering materials. Topological defects such as cyclic loops and dangling chains are ubiquitous in polymer networks. While fracture is a dominant mechanism for mechanical failures of polymer networks, existing models for fracture of polymer networks neglect the presence of topological defects. Here, we report a defect-network fracture model that accounts for the impact of various types of topological defects on fracture of polymer networks. We show that the fracture energy of polymer networks should account for the energy from multiple layers of polymer chains adjacent to the crack. We further show that the presence of topological defects tends to toughen a polymer network by increasing the effective chain length, yet to weaken the polymer network by introducing inactive polymer chains. Such competing effects can either increase or decrease the overall intrinsic fracture energy of the polymer network, depending on the types and densities of topological defects. Our model provides theoretical explanations for the experimental data on the intrinsic fracture energy of polymer networks with various types and densities of topological defects.

Scalable One-Pot-Liquid-Phase Oligonucleotide Synthesis for Model Network Hydrogels

Solid-phase oligonucleotide synthesis (SPOS) based on phosphoramidite chemistry is currently the most widespread technique for DNA and RNA synthesis but suffers from scalability limitations and high reagent consumption. Liquid-phase oligonucleotide synthesis (LPOS) uses soluble polymer supports and has the potential of being scalable. However, at present, LPOS requires 3 separate reaction steps and 4-5 precipitation steps per nucleotide addition. Moreover, long acid exposure times during the deprotection step degrade sequences with high A content (adenine) due to depurination and chain cleavage. In this work, we present the first one-pot liquid-phase DNA synthesis technique which allows the addition of one nucleotide in a one-pot reaction of sequential coupling, oxidation, and deprotection followed by a single precipitation step. Furthermore, we demonstrate how to suppress depurination during the addition of adenine nucleotides. We showcase the potential of this technique to prepare high-purity 4-arm PEG-T20 (T = thymine) and 4-arm PEG-A20 building blocks in multigram scale. Such complementary 4-arm PEG-DNA building blocks reversibly self-assemble into supramolecular model network hydrogels and facilitate the elucidation of bond lifetimes. These model network hydrogels exhibit new levels of mechanical properties (storage modulus, bond lifetimes) in DNA bonds at room temperature (melting at 44 °C) and thus open up pathways to next-generation DNA materials programmable through sequence recognition and available for macroscale applications.

Theory of Flexible Polymer Networks: Elasticity and Heterogeneities

A review of the main elasticity models of flexible polymer networks is presented. Classical models of phantom networks suggest that the networks have a tree-like structure. The conformations of their strands are described by the model of a combined chain, which consists of the network strand and two virtual chains attached to its ends. The distribution of lengths of virtual chains in real polydisperse networks is calculated using the results of the presented replica model of polymer networks. This model describes actual networks having strongly overlapping and interconnected loops of finite sizes. The conformations of their strands are characterized by the generalized combined chain model. The model of a sliding tube is represented, which describes the general anisotropic deformations of an entangled network in the melt. I propose a generalization of this model to describe the crossover between the entangled and phantom regimes of a swollen network. The obtained dependence of the Mooney-Rivlin parameters C 1 and C 2 on the polymer volume fraction is in agreement with experiments. The main results of the theory of heterogeneities in polymer networks are also discussed.

Polymer Networks: From Plastics and Gels to Porous Frameworks

Polymer networks, which are materials composed of many smaller components-referred to as "junctions" and "strands"-connected together via covalent or non-covalent/supramolecular interactions, are arguably the most versatile, widely studied, broadly used, and important materials known. From the first commercial polymers through the plastics revolution of the 20^th century to today, there are almost no aspects of modern life that are not impacted by polymer networks. Nevertheless, there are still many challenges that must be addressed to enable a complete understanding of these materials and facilitate their development for emerging applications ranging from sustainability and energy harvesting/storage to tissue engineering and additive manufacturing. Here, we provide a unifying overview of the fundamentals of polymer network synthesis, structure, and properties, tying together recent trends in the field that are not always associated with classical polymer networks, such as the advent of crystalline "framework" materials. We also highlight recent advances in using molecular design and control of topology to showcase how a deep understanding of structure-property relationships can lead to advanced networks with exceptional properties.

BigSMILES: A Structurally-Based Line Notation for Describing Macromolecules

Having a compact yet robust structurally based identifier or representation system is a key enabling factor for efficient sharing and dissemination of research results within the chemistry community, and such systems lay down the essential foundations for future informatics and data-driven research. While substantial advances have been made for small molecules, the polymer community has struggled in coming up with an efficient representation system. This is because, unlike other disciplines in chemistry, the basic premise that each distinct chemical species corresponds to a well-defined chemical structure does not hold for polymers. Polymers are intrinsically stochastic molecules that are often ensembles with a distribution of chemical structures. This difficulty limits the applicability of all deterministic representations developed for small molecules. In this work, a new representation system that is capable of handling the stochastic nature of polymers is proposed. The new system is based on the popular "simplified molecular-input line-entry system" (SMILES), and it aims to provide representations that can be used as indexing identifiers for entries in polymer databases. As a pilot test, the entries of the standard data set of the glass transition temperature of linear polymers (Bicerano, 2002) were converted into the new BigSMILES language. Furthermore, it is hoped that the proposed system will provide a more effective language for communication within the polymer community and increase cohesion between the researchers within the community.

Relative contributions of chain density and topology to the elasticity of two-dimensional polymer networks

Understanding the relationships between the structure of polymer networks and their mechanical properties is important for the design of advanced soft materials with optimal properties. However, classical rubber elasticity theories often fall short in their description of the network structure, while simulation techniques at molecular scale remain impractical at that length scale. Here we develop a computational approach based on random discrete networks, in which the polymer network is represented as an assembly of non-linear springs connected at crosslinking points. The density of elastically-effective chains, average network coordination and chain contour lengths are varied independently in order to identify their respective contributions to the network elasticity. Numerical results suggest scaling relations between network parameters and elastic properties that are markedly different from the predictions of classical rubber elasticity theories. In particular, the elastic modulus of 2D random networks is found to be independent of density at constant topology, and proportional to the average coordination at constant density. The discrepancy is due to the pre-straining of the chains in the discrete network, which is not accounted for in classical models of rubber elasticity. Our results have implications for the interpretation of experimental data for ideal network gels that are formed by the cross-coupling of macromolecular building blocks in solution.

Exploiting the conformational-selection mechanism to control the response kinetics of a "smart" DNA hydrogel

The sequence-specific hybridization and molecular recognition properties of DNA support the construction of stimulus-responsive hydrogels with precisely controlled crosslink geometry. Here we show that, as predicted by the conformational selection mechanism, the response kinetics of such a hydrogel can be tuned over orders of magnitude by modulating the thermodynamic stability of its crosslinks.

Spectroscopic and Rheological Cross-Analysis of Polyester Polyol Cure Behavior: Role of Polyester Secondary Hydroxyl Content

The sol-gel transition of a series of polyester polyol resins possessing varied secondary hydroxyl content and reacted with a polymerized aliphatic isocyanate cross-linking agent is studied to elucidate the effect of molecular architecture on cure behavior. Dynamic rheology is utilized in conjunction with time-resolved variable-temperature Fourier-transform infrared spectroscopy to examine the relationship between chemical conversion and microstructural evolution as functions of both time and temperature. The onset of a percolated microstructure is identified for all resins, and apparent activation energies extracted from Arrhenius analyses of gelation and average reaction kinetics are found to depend on the secondary hydroxyl content in the polyester polyols. The similarity between these two activation energies is explored. Gel point suppression is observed in all the resin systems examined, resulting in significant deviations from the classical gelation theory of Flory and Stockmayer. The magnitude of these deviations depends on secondary hydroxyl content, and a qualitative model is proposed to explain the observed phenomena, which are consistent with results previously reported in the literature.

On the sensitivity of alginate rheology to composition

The linear response of alginate-phenyl boronic acid (Alg-PBA) esters shows a universal, composition-independent viscoelastic fluid-like behaviour. Reversible association of alginates governs their rheology at all compositions (viz. at all alginate concentrations and solution pH). However, their high strain behaviour is very sensitive to composition. Tuning composition affords liquids that neck to form filaments capable of being drawn to large elongations without failure. We interpret our data by invoking strain-dependent association and dissociation rates for the alginates. High association rates at high strain result in materials with viscoelastic liquid like behaviour.

Direct characterization of a polymer network through its retainable units

A partially decrosslinkable network provides a general protocol for full, direct and quantitative characterization of polymer networks through its retainable units.

Nanonetwork photogrowth expansion: Tailoring nanoparticle networks’ chemical structure and local topology

Parent nanoparticle networks containing trithiocarbonate photoactive groups form nanonetworks with incorporated homopolymers, random copolymers and block copolymers through a developed photogrowth expansion process.