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Recent experiments on self-diffusion in associative networks have shown superdiffusive scaling hypothesized to originate from molecular diffusive mechanisms, which include walking and hopping of th...

The failure properties of a polymer network, including toughness, ultimate strain, and ultimate stress, are some of the most critical properties for network performance. The polymer networks often ...

In the classical phantom network theory, the shear modulus of a polymer network is derived assuming the underlying network has a treelike topology made up of identical strands. However, in real networks, defects such as dangling ends, cyclic defects, and polydispersity in strand sizes exist. Moreover, studies have shown that cyclic defects, or loops, are intrinsic to polymer networks. In this study, we illustrate a general framework for calculating the rubber elasticity of phantom networks with arbitrary defects. Closed form solutions for the elastic effectiveness of strands near isolated loops and dangling ends are obtained, and it was found that under classical assumptions of phantom network theory loops with order ≥3 have zero net impact on the overall elasticity. However, when a simple approximation for strand prestrain is considered, the modified network theory agrees well with experimentally measured moduli of PEG gels.

End-block association dynamics are known to influence deformation behavior in block copolymer systems. The ability to obtain precisely sequence controlled systems can help inform this deformation behavior, which is often influenced by dispersity in sequence and molar mass. Elastin-like polypeptides (ELPs) are a class of protein that consists of a sequence of five amino acids (XPGVG) that thermoresponsively aggregate in solution. These ELPs can be used as end-blocks in triblock fusion proteins with coiled-coil associating midblock domains to result in dual-associating, network-forming materials. By modifying the standard glycine-containing ELP sequence (XPGVG) to instead contain alanine in the third position of the repeat sequence (XPAVG), it is possible to improve the properties of the material in both shear and extension. In extension at 50 °C, the alanine-containing triblock (A10P4A10) and the glycine-containing triblock (G10P4G10) have similar Young’s moduli. However, while G10P4G10 yields and breaks w...

Recent experiments have revealed that a variety of associative polymers with different architecture (linear and branched) and different nature of the associating interaction (associative protein domains and metal–ligand bonds) exhibit unexplained superdiffusive behavior. Here, Brownian dynamics simulations of unentangled coarse-grained associating star-shaped polymers are used to establish a molecular picture of chain dynamics that explains this behavior. Polymers are conceptualized as particles with effective Rouse diffusivities that interact with a mean field background through attachments by stickers at the end of massless springs that represent the arms of the polymer. The simulations reveal three mechanisms of molecular diffusion at length scales much larger than the radius of gyration: hindered diffusion, walking diffusion, and molecular hopping, all of which depend strongly on polymer concentration, arm length, and the association/dissociation rate constants. The molecular model establishes that su...

Gels formed by coupling two different four-arm star polymers lead to polymer networks with high strength and low spatial heterogeneity. However, like all real polymer networks, these materials contain topological defects which affect their properties. In this study, kinetic graph theory and Monte Carlo simulation are used to investigate the structure and cyclic defects formed via A–B type end-linking of symmetric tetra-arm star polymer precursors. While loops constituting of odd number of junctions are forbidden by precursor chemistry, the amount and the correlation of secondary loops are found to increase with decreasing precursor concentration. This suppresses gelation, and the delay of gel point is quantitatively predicted by the topological simulations. Furthermore, comparison with network formed with asymmetric bifunctional–tetrafunctional precursors revealed that the behavior of loops consisting of 2n junctions in the symmetric system is analogous to the behavior of loops consisting of n junctions i...

The junction functionality of polymer networks is a key design variable to tune the material properties through changing the network connectivity. Here, we perform a Monte Carlo simulation to study the topology and elasticity of end-linked polymer networks constructed by junctions with different functionalities. The effect of junction functionality on the topological structure of the network displays both universal features and odd–even effects. For all junction functionalities, the primary loop fraction shows a linear dependence on the dimensionless product of concentration with single chain pervaded volume. The slopes of the lines exhibit strong odd–even alternation: primary loops are formed more frequently for junctions with an odd number of functional groups. The secondary loop fraction has a maximum when plotted against the normalized primary loop fraction, where the value of the maximum also shows odd–even alternation. The topological information obtained through Monte Carlo simulation is then incor...

Understanding the quantitative relationship between the dynamic mechanical properties of associating polymer networks and the dynamics of sticker bonds represents an important problem in polymer science because materials mechanics is affected by not only the sticker bond chemistry but also the sticker position, the polymer structure, and the physical environment of the associating polymers such as concentration and solvent quality. In this study, associating networks formed by structurally well-defined linear poly(N,N-dimethylacrylamide) polymers with histidine side groups in complexation with Ni2+ ions are chosen as a model system. “Sticker diffusion and dissociation spectrometry” is developed as a new method to quantify the dissociation dynamics of stickers within the network environment where the stickers are covalently attached to polymers above their overlap concentration. The estimated time constants for junction dissociation in gels are shown to be substantially different than the ones measured by ...

The dynamics of associating bonds in transient polymer networks exerts a paramount influence on their relaxation and time-dependent mechanical properties. In particular, diffusive motion of polymers mediated by the dissociation and association equilibrium of reversible junctions can affect the materials’ structural stability, dynamic mechanical properties, and a broad spectrum of functionality that arises from the constant motion of polymer chains. In this work, forced Rayleigh scattering is used to measure the diffusion of terpyridine end-functionalized four-arm poly(ethylene glycol) polymers transiently interlinked by zinc ions in organic solvent across a wide range of length and time scales. Phenomenological superdiffusion, where the scaling of the squared length dimension vs time has a power-law exponent larger than one, is demonstrated as an intrinsic feature of these networks due to the interplay of chain dissociation and diffusion. Outside the superdiffusive regime, normal Fickian diffusion is reco...

Through the use of macromolecular design and efficient chemical reactions it is now possible to control the composition of polymer networks and gels with excellent precision. In contrast, topological defects are still impossible to avoid and are generally difficult to quantify. For example, primary loops that form when a bifunctional monomer (A2) reacts twice with the same f functional (f > 2) monomer (Bf) during formation of an end-linked A2 + Bf network represent a pervasive defect that has a detrimental effect on mechanical integrity. Methods for the quantitative analysis of primary loops in such materials have recently emerged; however, these methods have only been applied to the simplest network structure: A2 + B3. Herein, we report strategies for counting primary loops in tetrafunctional (A2 + B4) networks and networks with mixed tri- and tetrafunctional (A2 + B3/B4) junctions. We apply these strategies to the quantitative analysis of primary loops in a series of end-linked poly(ethylene glycol) hyd...

Understanding dynamic relaxation mechanisms in self-diffusion and constraint release processes of rod–coil block copolymers is important for many technological applications that employ neat melts or concentrated solutions. Using a model system composed of poly(alkoxyphenylenevinylene) rods and polyisoprene coils, reptation theories of entangled rod–coil block copolymers are investigated in the isotropic melt state. Self-diffusion was measured by forced Rayleigh scattering using a red laser line and a new blue photoswitchable dye that allow operation above the bandgap of most semiconducting polymers. In contrast to previous tracer studies where the diffusion of rod–coils through a coil homopolymer matrix is slowed relative to coil homopolymers because of a mismatch in the curvature of the rod and coil entanglement tubes, slowed diffusion is only present in self-diffusion measurements above a critical molecular weight. An activated reptation mechanism with constraint release is proposed as a modification to...

Polymers exhibiting lower critical solution behavior in water have found broad use as thermoresponsive moieties in soft materials, particularly in biomedical applications for triggered actuation, gelation, accumulation, or release. In this work, changing the thermoresponsive block in a self-assembling hydrogel is shown to be a useful approach to control the viscoelastic behavior and mechanical reinforcement of the gel above its transition temperature. Triblock copolymers were prepared with artificial associative protein midblocks from either site-specific bioconjugation of narrowly disperse poly(N-isopropylacrylamide) (PNIPAM) or as biosynthetic genetic fusions to monodisperse elastin-like polypeptide (ELP) sequences. Both synthetic approaches yield responsively reinforceable hydrogels that can be stiffened by up to an order of magnitude to approximately 105 Pa at 30% (w/w). However, end block chemical composition and linear block copolymer architecture could be manipulated to yield high-temperature plate...

Stimuli-responsive photonic gels are made from the lamellar block copolymer (BCP) poly(styrene-b-2-vinylpyridine) (PS–P2VP), where the photonic responses are triggered by swelling/deswelling of the P2VP block with a selective solvent. When compared to isotropic swelling in chemically cross-linked homopolymer gels, the P2VP block in the lamellar BCP shows significantly lower degrees of swelling in alcohol–water cosolvents. The glassy PS layers completely constrain the lateral expansion of the P2VP gel layers and the dislocation defect network that develops during BCP self-assembly provides a counter force to vertical swelling. A model based on Flory–Huggins mixing and dislocation network strain energy is proposed to capture the swelling behavior of the BCP and is then used to estimate the dislocation network density in the lamellar BCP. This work establishes the quantitative relationship between the reflective color of the photonic gel, the effective χ parameter of the swellable block and the solvent, and ...

Mechanisms of entangled rod–coil diblock copolymer diffusion are investigated using tracer diffusion simulations and experiments in a matrix of entangled coil homopolymers, demonstrating that the d...

A new method to achieve long-range orientational order in symmetric diblock copolymer nanodomains through the alignment and chaining of superparamagnetic nanoparticles in a magnetic field is investigated computationally and theoretically. The effects of nanoparticle size, volume fraction, and magnetization strength are explored using the hybrid particle field (HPF) technique for particles that selectively segregate into one domain of a symmetric diblock copolymer assembly. A critical selectivity of the particles for one nanodomain is observed, above which strong alignment results and below which comparatively disordered structures are formed. The 2D simulations reveal that, for a given nanoparticle volume fraction, only a nanoparticle size commensurate with the block copolymer domain spacing yields well-aligned nanostructures. Nanoparticles significantly larger than the domain spacing break the symmetry of the lamellar phase and result in poor alignment, while high defect densities are observed for smalle...

The use of ionic interactions to direct both protein templating and block copolymer self-assembly into nanopatterned films with only aqueous processing conditions is demonstrated using block copolymers containing both thermally responsive and pH responsive blocks. Controlled reversible addition-fragmentation chain-transfer (RAFT) polymerization is employed to synthesize poly(N-isopropylacrylamide-b-2-(dimethylamino)ethyl acrylate) (PNIPAM-b-PDMAEA) diblock copolymers. The pH-dependent ionic complexation between the fluorescent protein, mCherry, and the ionic PDMAEA block is established using dynamic light scattering (DLS) and UV-Vis spectroscopy. DLS shows that the size of the resulting coacervate micelles depends strongly on pH, while UV-Vis spectroscopy shows a correlation between the protein’s absorption maximum and the ionic microenvironment. Zeta potential measurements clearly indicate the ionic nature of the complex-forming interactions. Spin casting was used to prepare nanostructured films from the protein-block copolymer coacervates. After film formation, the lower critical solution temperature (LCST) of the PNIPAM blocks allows the nanomaterial to be effectively immobilized in aqueous environments at physiological temperatures, enabling potential use as a controlled protein release material or polymer matrix for protein immobilization. At pH 9.2 and 7.8, the release rates are at least 10 times faster than that at pH 6.4 due to weaker interaction between protein and PNIPAM-b-PDMAEA (PND) diblock copolymer. Due to the ionic environment in which protein is confined, the majority of the protein (80%) remains active, independent of pH, even after having been dehydrated in vacuum and confined in the films.

The Flory−Huggins interaction is measured for a model rod−coil block copolymer system, poly(alkoxyphenylenevinylene-b-isoprene), by fitting the interfacial segregation of block copolymer to a homopolymer interface and by using the random phase approximation (RPA) for block copolymers. The measured interfacial segregation of a block copolymer to the interface between homopolymers, fit with a self-consistent field theory (SCFT) simulation using χ as a variable parameter, gives a functional form χ = 34.8/T − 0.091. When RPA is applied to neutron scattering curves for the rod−coil system above the order−disorder transition, the theoretical structure factors are inconsistent with observed scattering curves due to complex aggregated structures formed in the nematic and isotropic states. Using the Flory−Huggins parameter and a previously measured value of the Maier−Saupe parameter, the PPV-b-PI phase diagram may be converted from system-specific variables to dimensionless parameters. Under the assumptions that t...

The rod orientation and crystalline packing of a model semiconducting rodlike polymer, poly(2,5-di(2‘-ethylhexyloxy)-1,4-phenylenevinylene) (DEH−PPV), is shown to affect the self-assembly of weakly segregated rod−coil block copolymers. The in-plane packing of DEH−PPV rods in lamellar poly(2,5-di(2‘-ethylhexyloxy)-1,4-phenylenevinylene-b-isoprene) (DEH−PPV-b-PI) diblock copolymers is nearly identical to that observed in DEH−PPV homopolymers for compositions ranging from 0.42 to 0.82 vol % coil block. The crystal structure of DEH−PPV, characterized by grazing incidence X-ray diffraction and electron diffraction, consists of a tetragonal unit cell having c = 0.665 nm with a = b = 1.348 nm. The polymer chain axis is aligned along the [001] direction, and the nearest neighbor rod−rod spacing along 〈110〉 is 1.0 nm. As-cast thin films of DEH−PPV homopolymer demonstrate chain alignment primarily perpendicular to the substrate in 5100 g/mol homopolymer, while for 3500 g/mol homopolymer the chains align both perpen...

A new phase consisting of rectangular rod nanodomains packed onto a hexagonal lattice is observed in rod−coil block copolymers at the limit of both large volume fraction asymmetry and large geometrical asymmetry between the rod and coil. In moderately segregated poly(alkoxyphenylenevinylene-b-isoprene) (PPV-b-PI), an order−order transition is observed between hexagonal and lamellar phases for polymers near the phase boundary, and the lamellar phase is observed at high temperatures. The domain spacings of polymers in the lamellar phase collapse on to a simple scaling relationship where domain spacing is proportional to molecular weight. The proportionality constant is equal to the statistical segment length of the PPV rod block, suggesting that the angle between the rod director and the lamellar interface is nearly 90°. At higher temperatures, the block copolymers transition from ordered to nematic to isotropic states, with the intermediate nematic phase being observed for all coil fractions studied. A thr...

The addition of homopolymers to a self-assembling rod-coil block copolymer is demonstrated to be a flexible route toward domain size control. Molecular weight matched rod-like homopolymers interdigitate with the rod-blocks within their respective lamellae. As a result of the interdigitation, the coil blocks must rearrange to occupy more interfacial area resulting in an unprecedented decrease in domain spacing with increasing rod homopolymers. Conversely coil homopolymers were locally solubilized within the coil microdomain resulting in an increase of domain spacing with increasing coil homopolymers. The mechanisms of homopolymers solubilization are in qualitative agreement with predictions made by self-consistent mean-field theory (SCFT) calculations.

Poly(alkoxyphenylenevinylene-b-isoprene) (PPV-b-PI) rod−coil block copolymers demonstrate novel structures due to the rodlike PPV block. Thin films of the polymers self-assemble into lamellar microphases upon thermal annealing with the lamellae oriented primarily parallel to the substrate. The parallel lamellae show symmetric wetting of PI at both the substrate and vacuum interfaces. Grains of lamellae with parallel orientation are characterized by irregular polygon shapes and are bounded by defect regions where the lamellae are oriented out of the plane of the film. Grazing-incidence small-angle X-ray scattering (GISAXS) shows that these out-of-plane lamellae are strongly oriented perpendicular to the film. The perpendicular lamellae are much straighter than those typically observed in coil−coil block copolymers due to the high bending energy of the liquid crystalline rod nanodomains. Islands or holes form in the films, and domain spacings estimated from the island/hole heights are equal to the bulk doma...

Poly(alkoxyphenylenevinylene-b-isoprene) is used to study the phase transitions of a weakly segregated rod−coil block copolymer system. In the high coil fraction region of the phase diagram, phase transitions are caused by relatively small changes in temperature and composition. Several different sequences of phase transitions are observed, allowing fine control of structure, orientation, and thermal history effects. Weakly segregated symmetric rod−coil block copolymers organize into lamellar microphases at low temperature and disorder into nematic and isotropic phases with increasing temperature. As the coil fraction is increased, the lamellar structure loses long-range order but the microphase structure does not change. In these asymmetric block copolymers, a distinct change in phase transitions upon heating is observed. The stable nematic window narrows as the coil fraction increases. As a result, while symmetric block copolymers transition from a lamellar to an intermediate nematic and finally to an i...

Monodisperse, low molecular weight poly(2,5-di(2‘-ethylhexyloxy)-1,4-phenylenevinylene) (DEH-PPV) demonstrates significantly better structural order than polydisperse PPVs. Since optical and electr...