Forensics of polymer networks.

Our lives cannot be imagined without polymer networks, which range widely, from synthetic rubber to biological tissues. Their properties-elasticity, strain-stiffening and stretchability-are controlled by a convolution of chemical composition, strand conformation and network topology. Yet, since the discovery of rubber vulcanization by Charles Goodyear in 1839, the internal organization of networks has remained a sealed 'black box'. While many studies show how network properties respond to topology variation, no method currently exists that would allow the decoding of the network structure from its properties. We address this problem by analysing networks' nonlinear responses to deformation to quantify their crosslink density, strand flexibility and fraction of stress-supporting strands. The decoded structural information enables the quality control of network synthesis, comparison of targeted to actual architecture and network classification according to the effectiveness of stress distribution. The developed forensic approach is a vital step in future implementation of artificial intelligence principles for soft matter design.

Mimicking biological stress-strain behaviour with synthetic elastomers.

Despite the versatility of synthetic chemistry, certain combinations of mechanical softness, strength, and toughness can be difficult to achieve in a single material. These combinations are, however, commonplace in biological tissues, and are therefore needed for applications such as medical implants, tissue engineering, soft robotics, and wearable electronics. Present materials synthesis strategies are predominantly Edisonian, involving the empirical mixing of assorted monomers, crosslinking schemes, and occluded swelling agents, but this approach yields limited property control. Here we present a general strategy for mimicking the mechanical behaviour of biological materials by precisely encoding their stress-strain curves in solvent-free brush- and comb-like polymer networks (elastomers). The code consists of three independent architectural parameters-network strand length, side-chain length and grafting density. Using prototypical poly(dimethylsiloxane) elastomers, we illustrate how this parametric triplet enables the replication of the strain-stiffening characteristics of jellyfish, lung, and arterial tissues.

Sugar-Based Polymers with Stereochemistry-Dependent Degradability and Mechanical Properties.

Stereochemistry in polymers can be used as an effective tool to control the mechanical and physical properties of the resulting materials. Typically, though, in synthetic polymers, differences among polymer stereoisomers leads to incremental property variation, i.e., no changes to the baseline plastic or elastic behavior. Here we show that stereochemical differences in sugar-based monomers yield a family of nonsegmented, alternating polyurethanes that can be either strong amorphous thermoplastic elastomers with properties that exceed most cross-linked rubbers or robust, semicrystalline thermoplastics with properties comparable to commercial plastics. The stereochemical differences in the monomers direct distinct intra- and interchain supramolecular hydrogen-bonding interactions in the bulk materials to define their behavior. The chemical similarity among these isohexide-based polymers enables both statistical copolymerization and blending, which each afford independent control over degradability and mechanical properties. The modular molecular design of the polymers provides an opportunity to create a family of materials with divergent properties that possess inherently built degradability and outstanding mechanical performance.

Ultra-Tough Elastomers from Stereochemistry-Directed Hydrogen Bonding in Isosorbide-Based Polymers.

The remarkable elasticity and tensile strength found in natural elastomers are challenging to mimic. Synthetic elastomers typically feature covalently cross-linked networks (rubbers), but this hinders their reprocessability. Physical cross-linking via hydrogen bonding or ordered crystallite domains can afford reprocessable elastomers, but often at the cost of performance. Herein, we report the synthesis of ultra-tough, reprocessable elastomers based on linear alternating polymers. The incorporation of a rigid isohexide adjacent to urethane moieties affords elastomers with exceptional strain hardening, strain rate dependent behavior, and high optical clarity. Distinct differences were observed between isomannide and isosorbide-based elastomers where the latter displays superior tensile strength and strain recovery. These phenomena are attributed to the regiochemical irregularities in the polymers arising from their distinct stereochemistry and respective inter-chain hydrogen bonding.

Sierpinski Pyramids by Molecular Entanglement.

Planar, terpyridine-based metal complexes with the Sierpinski triangular motif and alkylated corners undergo a second self-assembly event to give megastructural Sierpinski pyramids; assembly is driven by the facile lipophilic-lipophilic association of the alkyl moieties and complementary perfect fit of the triangular building blocks. Confirmation of the 3D, pyramidal structures was verified and supported by a combination of TEM, AFM, and multiscale simulation techniques.

Elastocapillarity and rolling dynamics of solid nanoparticles on soft elastic substrates.

The motion of nanoparticles on soft surfaces is the result of interplay between capillary, elastic and friction forces. To elucidate the importance of the different contributions controlling nanoparticle rolling dynamics on soft surfaces, we performed molecular dynamics simulations of solid nanoparticles in contact with soft elastic substrates. The nanoparticle motion is initiated by applying a constant force resulting in stationary, steady rolling, and accelerating states, depending on the nanoparticle-substrate work of adhesion, W, the magnitude of the net applied force, F, and the substrate shear modulus G. In the stationary state, the restoring torque produced in the contact area balances the torque due to the external force. The rolling force Fr, determining the crossover to the rolling state, is proportional to the product of the work of adhesion W and nanoparticle size Rp, Fr ∼ WRp. In the steady rolling state, F > Fr, the nanoparticle maintains a constant rolling velocity which is a manifestation of the balance between the rolling friction force and the applied force. The observed scaling relationships between the applied force and nanoparticle velocity reflect a viscoelastic nature of the substrate deformation dynamics. A nanoparticle begins to accelerate when the energy supplied to the nanoparticle exceeds the energy dissipated in the contact area due to viscoelastic substrate deformation. Using these simulation results, we have constructed a diagram of states in terms of the dimensionless parameters F/WRp and W/GRp.

Entropy-driven segregation of polymer-grafted nanoparticles under confinement.

The modification of nanoparticles with polymer ligands has emerged as a versatile approach to control the interactions and organization of nanoparticles in polymer nanocomposite materials. Besides their technological significance, polymer-grafted nanoparticle (PGNP) dispersions have attracted interest as model systems to understand the role of entropy as a driving force for microstructure formation. For instance, densely and sparsely grafted nanoparticles show distinct dispersion and assembly behaviors within polymer matrices due to the entropy variation associated with conformational changes in brush and matrix chains. Here we demonstrate how this entropy change can be harnessed to drive PGNPs into spatially organized domain structures on submicrometer scale within topographically patterned thin films. This selective segregation of PGNPs is induced by the conformational entropy penalty arising from local perturbations of grafted and matrix chains under confinement. The efficiency of this particle segregation process within patterned mesa-trench films can be tuned by changing the relative entropic confinement effects on grafted and matrix chains. The versatility of topographic patterning, combined with the compatibility with a wide range of nanoparticle and polymeric materials, renders SCPINS (soft-confinement pattern-induced nanoparticle segregation) an attractive method for fabricating nanostructured hybrid films with potential applications in nanomaterial-based technologies.

Gluing Interfaces with Soft Nanoparticles.

Nanoparticles have been recently shown to be able to act as effective adhesives capable of binding two soft materials together. We performed coarse-grained molecular dynamics simulations to study contact mechanics of soft nanoparticles at the interfaces between two elastic surfaces. Depending on the nanoparticle size as well as the substrates' elastic and interfacial properties, a nanoparticle at the interface between two elastic substrates could be in a bridging or Pickering state. The degree of penetration of a nanoparticle into a substrate is shown to be determined by nanoparticle size, strength of nanoparticle-substrate interactions, and nanoparticle and substrate elastic properties. Using the weighted histogram analysis method, we calculated the potential of mean force for separation of two substrates whose interface was reinforced by deformable nanoparticles. These simulations show that interface reinforcement is a function of nanoparticle size and elastic modulus. The most effective reinforcement of the interface was observed for the softest nanoparticles which could result in close to 8 times increase in the work of adhesion.

Molecular Dynamics Simulations of Surface and Interfacial Tension of Graft Polymer Melts.

Understanding the surface properties of polymer melts is crucial for designing new polymeric coatings, adhesives, and composites. Here, we study the effect of molecular architecture on surface and interfacial tension of melts of graft and linear polymers by molecular dynamics simulations. In particular, we elucidate the effect of the degree of polymerization of the side chains nsc and their grafting density 1/ ng on the surface tension of the graft polymer/vacuum interface, γG, and the interfacial tension of the interface between graft and linear polymer melts, γGL. For the case of the graft polymer/vacuum interface, our simulations confirm that the surface tension is a linear function of the fraction of the backbone ends fbe and side chain ends fse, γG = γ∞ - γbe fbe - Δγ fse, where γ∞ is the surface tension of the system of graft polymers with infinite molecular weight and γbe and Δγ are surface tension contributions from backbone ends and difference between contributions coming from the side chain ends and grafting points, respectively. This dependence of the surface tension highlights the entropic origin of the surface tension corrections associated with the redistribution of the grafting points and ends at the interface. However, the interfacial tension of the interface between graft and linear polymer melts does not show any significant dependence on the molecular structure of the graft polymers, thus pointing out the dominance of enthalpic contribution to the interfacial tension.

Surface Stresses and a Force Balance at a Contact Line.

Results of the coarse-grained molecular dynamics simulations are used to show that the force balance analysis at the triple-phase contact line formed at an elastic substrate has to include a quartet of forces: three surface tensions (surface free energies) and an elastic force per unit length. In the case of the contact line formed by a droplet on an elastic substrate an elastic force is due to substrate deformation generated by formation of the wetting ridge. The magnitude of this force fel is proportional to the product of the ridge height h and substrate shear modulus G. Similar elastic line force should be included in the force analysis at the triple-phase contact line of a solid particle in contact with an elastic substrate. For this contact problem elastic force obtained from contact angles and surface tensions is a sum of the elastic forces acting from the side of a solid particle and an elastic substrate. By considering only three line forces acting at the triple-phase contact line, one implicitly accounts the bulk stress contribution as a part of the resultant surface stresses. This "contamination" of the surface properties by a bulk contribution could lead to unphysically large values of the surface stresses in soft materials.

Solvent-free, supersoft and superelastic bottlebrush melts and networks.

Polymer gels are the only viable class of synthetic materials with a Young's modulus below 100 kPa conforming to biological applications, yet those gel properties require a solvent fraction. The presence of a solvent can lead to phase separation, evaporation and leakage on deformation, diminishing gel elasticity and eliciting inflammatory responses in any surrounding tissues. Here, we report solvent-free, supersoft and superelastic polymer melts and networks prepared from bottlebrush macromolecules. The brush-like architecture expands the diameter of the polymer chains, diluting their entanglements without markedly increasing stiffness. This adjustable interplay between chain diameter and stiffness makes it possible to tailor the network's elastic modulus and extensibility without the complications associated with a swollen gel. The bottlebrush melts and elastomers exhibit an unprecedented combination of low modulus (∼100 Pa), high strain at break (∼1,000%), and extraordinary elasticity, properties that are on par with those of designer gels.

Contact Mechanics of Nanoparticles: Pulling Rigid Nanoparticles from Soft, Polymeric Surfaces.

Detachment of rigid nanoparticles from soft, gel-like polymeric surfaces is studied by using a combination of the molecular dynamics simulations and theoretical calculations. Simulations show that detachment of nanoparticles from soft surfaces proceeds through a neck formation. Analysis of the simulation results demonstrates that the magnitude of the detachment force f* depends on the nanoparticle radius R(p), shear modulus of substrate G(s), surface tension of substrate γ(s), and work of adhesion W. It is controlled by the balance of the elastic energy, surface energy of the neck, and nanoparticle adhesion energy to a substrate and depends on the dimensionless parameter δ ∝ γ(s)(G(s)R(p))(-1/3)W(-2/3). In the case of small values of the parameter δ ≪ 1, the critical detachment force approaches a critical detachment force calculated by Johnson, Kendall, and Roberts for adhesive contact, f* = 1.5πWR(p). However, in the opposite limit, corresponding to soft substrates, for which δ ≫ 1, the critical detachment force f* ∝ γ(s)(3/2)R(p)(1/2)G(s)(-1/2). All simulation data can be described by a scaling function f* ∝ γ(s)(3/2)R(p)(1/2)G(s)(-1/2)δ(-1.89).

Adhesion and wetting of soft nanoparticles on textured surfaces: transition between Wenzel and Cassie-Baxter states.

We use a combination of the molecular dynamics simulations and scaling analysis to study interactions between gel-like nanoparticles and substrates covered with rectangular shape posts. Our simulations have shown that nanoparticles in contact with substrate undergo a first-order transition between the Cassie­Baxter and Wenzel states, which depends on nanoparticle shear modulus, the strength of nanoparticle­substrate interactions, height of the substrate posts, and nanoparticle size, Rp. There is a range of system parameters where these two states coexist such that the average indentation δ produced by substrate posts changes with nanoparticle shear modulus, Gp. We have developed a scaling model that describes deformation of nanoparticle in contact with patterned substrate. In the framework of this model, the effect of the patterned substrate can be taken into account by introducing an effective work of adhesion, Weff, which describes the first-order transition between Wenzel and Cassie­Baxter states. There are two different shape deformation regimes for nanoparticles with shear modulus Gp and surface tension γp. The shape of small nanoparticles with size Rp < γp(3/2)Gp(-1)Weff(-1/2) is controlled by capillary forces, while deformation of large nanoparticles, Rp > γp(3/2)Gp(-1)Weff(-1/2), is determined by nanoparticle elastic and contact free energies. The model predictions are in good agreement with simulation results.

Perfect mixing of immiscible macromolecules at fluid interfaces.

The difficulty of mixing chemically incompatible substances--in particular macromolecules and colloidal particles--is a canonical problem limiting advances in fields ranging from health care to materials engineering. Although the self-assembly of chemically different moieties has been demonstrated in coordination complexes, supramolecular structures, and colloidal lattices among other systems, the mechanisms of mixing largely rely on specific interfacing of chemically, physically or geometrically complementary objects. Here, by taking advantage of the steric repulsion between brush-like polymers tethered to surface-active species, we obtained long-range arrays of perfectly mixed macromolecules with a variety of polymer architectures and a wide range of chemistries without the need of encoding specific complementarity. The net repulsion arises from the significant increase in the conformational entropy of the brush-like polymers with increasing distance between adjacent macromolecules at fluid interfaces. This entropic-templating assembly strategy enables long-range patterning of thin films on sub-100 nm length scales.

Nucleation-controlled polymerization of nanoparticles into supramolecular structures.

Controlled assembly of inorganic nanoparticles (NPs) into structurally defined supramolecular polymers will create nanomaterials with new collective properties. However, supramolecular polymerization of isotropic NPs remains a challenge because of the lack of anisotropic interactions in these monomers to undergo directional associations for the cooperative growth of supramolecular chains. Herein we report self-assembly behavior of poly(l-glutamic acid)-grafted gold NPs in solution and describe how combined attractive and repulsive interactions influence the shape and size of the resulting supramolecular assemblies. The study shows that the chain growth of supramolecular polymers can be achieved from the NP monomers and the process occurs in two distinct stages, with a slow nucleation step followed by a faster chain propagation step. The resulting supramolecular structures depend on both the grafting density of the poly(l-glutamic acid) on the NPs and the size of the NPs.

Viscosity of Polymer Solutions and Molecular Weight Characterization.

Since the pioneering research by Staudinger on dilute solution viscosity and its relation to the polymer molecular weight, viscosity analysis has become a valuable technique for polymer characterization. The conventional approach is based on the Huggins approximation of the solution-specific viscosity by a quadratic function of concentration, c. We show how to reformulate this approach in a universal form by representing a solution-specific viscosity, ηsp, as a generalized universal function ηsp(c) = α(c/c*) + (1 - α)(c/c*)2 of chain overlap concentration, c*, determined at ηsp = 1, with numerical coefficients α = 0.745 ± 0.005 for good and 0.625 ± 0.008 for a θ solvent. This viscosity representation can be viewed as a calibration curve for molecular weight determination from a measurement of the solution viscosity at a given solution concentration. Furthermore, the molecular weight dependence of the overlap concentration provides a means for quantifying the polymer/solvent affinity and the solvent effect on chain flexibility. The extension of the approach to semidilute solutions opens a path for obtaining molecular weight in a broad concentration range without requiring a dilution and monitoring its change during the polymerization reaction from solution viscosity.

Coarse-Grained Artificial Intelligence for Design of Brush Networks.

The ability to synthesize elastomeric materials with programmable mechanical properties is vital for advanced soft matter applications. Due to the inherent complexity of hierarchical structure-property correlations in brush-like polymer networks, the application of conventional theory-based, so-called Human Intelligence (HI) approaches becomes increasingly difficult. Herein we developed a design strategy based on synergistic combination of HI and AI tools which allows precise encoding of mechanical properties with three architectural parameters: degrees of polymerization (DP) of network strands, nx, side chains, nsc, backbone spacers between side chains, ng. Implementing a multilayer feedforward artificial neural network (ANN), we took advantage of model-predicted structure-property cross-correlations between coarse-grained system code including chemistry specific characteristics S = [l, v, b] defined by monomer projection length l and excluded volume v, Kuhn length b of bare backbone and side chains, and architecture A = [nsc, ng, nx] of polymer networks and their equilibrium mechanical properties P = [G, ß] including the structural shear modulus G and firmness parameter ß. The ANN was trained by minimizing the mean-square error with Bayesian regularization to avoid overfitting using a data set of experimental stress-deformation curves of networks with brush-like strands of poly(n-butyl acrylate), poly(isobutylene), and poly(dimethylsiloxane) having structural modulus G < 50 kPa and 0.01 ≤ ß ≤ 0.3. The trained ANN predicts network mechanical properties with 95% confidence. The developed ANN was implemented for synthesis of model networks with identical mechanical properties but different chemistries of network strands.

Mechanochromism and Strain-Induced Crystallization in Thiol-yne-Derived Stereoelastomers.

Most elastomers undergo strain-induced crystallization (SIC) under tension; as individual chains are held rigidly in a fixed position by an applied strain, their alignment along the strain field results in a shift from strain-hardening (SH) to SIC. A similar degree of stretching is associated with the tension necessary to accelerate mechanically coupled, covalent chemical responses of mechanophores in overstretched chains, raising the possibility of an interplay between the macroscopic response of SIC and the molecular response of mechanophore activation. Here, thiol-yne-derived stereoelastomers doped covalently with a dipropiolate-derivatized spiropyran (SP) mechanophore (0.25-0.38 mol%) are reported. The material properties of SP-containing films are consistent with undoped controls, indicating that the SP is a reporter of the mechanical state of the polymer. Uniaxial tensile tests reveal correlations between mechanochromism and SIC, which are strain-rate-dependent. When mechanochromic films are stretched slowly to the point of mechanophore activation, the covalently tethered mechanophore remains trapped in a force-activated state, even after the applied stress is removed. Mechanophore reversion kinetics correlate with the applied strain rate, resulting in highly tunable decoloration rates. Because these polymers are not covalently crosslinked, they are recyclable by melt-pressing into new films, increasing their potential range of strain-sensing, morphology-sensing, and shape-memory applications.

Bottlebrush Thermoplastic Elastomers as Hot-Melt Pressure-Sensitive Adhesives.

Hot-melt pressure-sensitive adhesives (HMPSAs) are used in applications from office supplies to biomedical adhesives. The major component in HMPSA formulations is thermoplastic elastomers, such as styrene-based block copolymers, that provide both mechanical integrity and moldability. Since neat polymer networks are unable to establish an adhesive bond, large quantities of plasticizers and tackifiers are added. These additives enhance the adhesive performance but complicate the phase behavior and property stability of the pressure-sensitive adhesive. Herein, we introduce an alternative additive-free approach to HMPSA design based on self-assembly of bottlebrush graft-copolymers, where side chains behave as softness, strength, and viscoelasticity mediators. These systems maintain moldability of conventional thermoplastic elastomers, while architecturally disentangled bottlebrush network strands empower several benefits such as extreme softness for substrate wetting, low melt viscosity for molding and 3D-printing, and a broad frequency range of viscoelastic responses for adhesion regulation within almost four orders of magnitude. The brush graft-copolymers implement five independently controlled architectural parameters to regulate the Rouse time, work of adhesion, and debonding mechanisms.