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.

Single-Event Spectroscopy and Unravelling Kinetics of Covalent Domains Based on Cyclobutane Mechanophores.

Mechanochemical reactions that lead to an increase in polymer contour length have the potential to serve as covalent synthetic mimics of the mechanical unfolding of noncovalent "stored length" domains in structural proteins. Here we report the force-dependent kinetics of stored length release in a family of covalent domain polymers based on cis-1,2-substituted cyclobutane mechanophores. The stored length is determined by the size (n) of a fused ring in an [n.2.0] bicyclic architecture, and it can be made sufficiently large (>3 nm per event) that individual unravelling events are resolved in both constant-velocity and constant-force single-molecule force spectroscopy (SMFS) experiments. Replacing a methylene in the pulling attachment with a phenyl group drops the force necessary to achieve rate constants of 1 s-1 from ca. 1970 pN (dialkyl handles) to 630 pN (diaryl handles), and the substituent effect is attributed to a combination of electronic stabilization and mechanical leverage effects. In contrast, the kinetics are negligibly perturbed by changes in the amount of stored length. The independent control of unravelling force and extension holds promise as a probe of molecular behavior in polymer networks and for optimizing the behaviors of materials made from covalent domain polymers.

Mechanism Dictates Mechanics: A Molecular Substituent Effect in the Macroscopic Fracture of a Covalent Polymer Network.

The fracture of rubbery polymer networks involves a series of molecular events, beginning with conformational changes along the polymer backbone and culminating with a chain scission reaction. Here, we report covalent polymer gels in which the macroscopic fracture "reaction" is controlled by mechanophores embedded within mechanically active network strands. We synthesized poly(ethylene glycol) (PEG) gels through the end-linking of azide-terminated tetra-arm PEG (Mn = 5 kDa) with bis-alkyne linkers. Networks were formed under identical conditions, except that the bis-alkyne was varied to include either a cis-diaryl (1) or cis-dialkyl (2) linked cyclobutane mechanophore that acts as a mechanochemical "weak link" through a force-coupled cycloreversion. A control network featuring a bis-alkyne without cyclobutane (3) was also synthesized. The networks show the same linear elasticity (G' = 23-24 kPa, 0.1-100 Hz) and equilibrium mass swelling ratios (Q = 10-11 in tetrahydrofuran), but they exhibit tearing energies that span a factor of 8 (3.4 J, 10.6, and 27.1 J·m-2 for networks with 1, 2, and 3, respectively). The difference in fracture energy is well-aligned with the force-coupled scission kinetics of the mechanophores observed in single-molecule force spectroscopy experiments, implicating local resonance stabilization of a diradical transition state in the cycloreversion of 1 as a key determinant of the relative ease with which its network is torn. The connection between macroscopic fracture and a small-molecule reaction mechanism suggests opportunities for molecular understanding and optimization of polymer network behavior.

PolyDAT: A Generic Data Schema for Polymer Characterization.

Polymers are stochastic materials that represent distributions of different molecules. In general, to quantify the distribution, polymer researchers rely on a series of chemical characterizations that each reveal partial information on the distribution. However, in practice, the exact set of characterizations that are carried out, as well as how the characterization data are aggregated and reported, is largely nonstandard across the polymer community. This scenario makes polymer characterization data highly disparate, thereby significantly slowing down the development of polymer informatics. In this work, a proposal on how structural characterization data can be organized is presented. To ensure that the system can apply universally across the entire polymer community, the proposed schema, PolyDAT, is designed to embody a minimal congruent set of vocabulary that is common across different domains. Unlike most chemical schemas, where only data pertinent to the species of interest are included, PolyDAT deploys a multi-species reaction network construct, in which every characterization on relevant species is collected to provide the most comprehensive profile on the polymer species of interest. Instead of maintaining a comprehensive list of available characterization techniques, PolyDAT provides a handful of generic templates, which align closely with experimental conventions and cover most types of common characterization techniques. This allows flexibility for the development and inclusion of new measurement methods. By providing a standard format to digitalize data, PolyDAT serves not only as an extension to BigSMILES that provides the necessary quantitative information but also as a standard channel for researchers to share polymer characterization data.

Role of Chain Length in the Formation of Frank-Kasper Phases in Diblock Copolymers.

The phase behavior of poly(styrene)-b-poly(1,4-butadiene) diblock copolymers with a polymer block invariant degree of polymerization N[over ¯]_{b}≈800 shows no evidence of Frank-Kasper phases, in contrast to low molar mass diblock copolymers (N[over ¯]_{b}<100) with the same conformational asymmetry. A universal self-concentration crossover parameter N[over ¯]_{x}≈400 is identified, directly related to the crossover to entanglement dynamics in polymer melts. Mean-field behavior is recovered when N[over ¯]_{b}>N[over ¯]_{x}, while complex low symmetry phase formation is attributed to fluctuations and space-filling constraints, which dominate when N[over ¯]_{b}

Conformation of Network Strands in Polymer Gels.

Small angle neutron scattering was used to measure single chain radii of gyration of end-linked polymer gels before and after cross-linking to calculate the prestrain, which is the ratio of the average chain size in a cross-linked network to that of a free chain in solution. The prestrain increased from 1.06 ± 0.01 to 1.16 ± 0.02 as gel synthesis concentration decreased near the overlap concentration, indicating that the chains are slightly more stretched in the network than in solution. Dilute gels with higher loop fractions were found to be spatially homogeneous. Form factor and volumetric scaling analyses independently confirmed that elastic strands stretch by 2-23% from Gaussian conformations to create a space-spanning network, with increased stretching as network synthesis concentration decreases. Prestrain measurements reported here serve as a point of reference for network theories that rely on this parameter for the calculation of mechanical properties.

Reactivity-Guided Depercolation Processes Determine Fracture Behavior in End-Linked Polymer Networks.

The fracture of polymer networks is tied to the molecular behavior of strands within the network, yet the specific molecular-level processes that determine the mechanical limits of a network remain elusive. Here, the question of reactivity-guided fracture is explored in otherwise indistinguishable end-linked networks by tuning the relative composition of strands with two different mechanochemical reactivities. Increasing the substitution of less mechanochemically reactive ("strong") strands into a network comprising more reactive ("weak") strands has a negligible impact on the fracture energy until the strong strand content reaches approximately 45%, at which point the fracture energy sharply increases with strong strand content. This aligns with the measured strong strand percolation threshold of 48 ± 3%, revealing that depercolation, or the loss of a percolated network structure, is a necessary criterion for crack propagation in a polymer network. Coarse-grained fracture simulations agree closely with the tearing energy trend observed experimentally, confirming that weak strand scissions dominate the failure until the strong strands approach percolation. The simulations further show that twice as many strands break in a mixture than in a pure network.

Extending BigSMILES to non-covalent bonds in supramolecular polymer assemblies.

As a machine-recognizable representation of polymer connectivity, BigSMILES line notation extends SMILES from deterministic to stochastic structures. The same framework that allows BigSMILES to accommodate stochastic covalent connectivity can be extended to non-covalent bonds, enhancing its value for polymers, supramolecular materials, and colloidal chemistry. Non-covalent bonds are captured through the inclusion of annotations to pseudo atoms serving as complementary binding pairs, minimal key/value pairs to elaborate other relevant attributes, and indexes to specify the pairing among potential donors and acceptors or bond delocalization. Incorporating these annotations into BigSMILES line notation enables the representation of four common classes of non-covalent bonds in polymer science: electrostatic interactions, hydrogen bonding, metal-ligand complexation, and π-π stacking. The principal advantage of non-covalent BigSMILES is the ability to accommodate a broad variety of non-covalent chemistry with a simple user-orientated, semi-flexible annotation formalism. This goal is achieved by encoding a universal but non-exhaustive representation of non-covalent or stochastic bonding patterns through syntax for (de)protonated and delocalized state of bonding as well as nested bonds for correlated bonding and multi-component mixture. By allowing user-defined descriptors in the annotation expression, further applications in data-driven research can be envisioned to represent chemical structures in many other fields, including polymer nanocomposite and surface chemistry.

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.

Toughening hydrogels through force-triggered chemical reactions that lengthen polymer strands.

The utility and lifetime of materials made from polymer networks, including hydrogels, depend on their capacity to stretch and resist tearing. In gels and elastomers, those mechanical properties are often limited by the covalent chemical structure of the polymer strands between cross-links, which is typically fixed during the material synthesis. We report polymer networks in which the constituent strands lengthen through force-coupled reactions that are triggered as the strands reach their nominal breaking point. In comparison with networks made from analogous control strands, reactive strand extensions of up to 40% lead to hydrogels that stretch 40 to 50% further and exhibit tear energies that are twice as large. The enhancements are synergistic with those provided by double-network architectures and complement other existing toughening strategies.

Synthesis and Self-Assembly of ABn Miktoarm Star Polymers.

The stability of tetrahedrally close-packed (TCP) phases in block copolymer melts is predicted by theory to depend on molecular architecture, yet no experimental studies to date have probed its effect. Motivated by this open question, here we report an efficient synthesis of asymmetric ABn miktoarm star polymers using functionalized sugars as cores for orthogonal grafting-from block copolymerizations. A combination of ring-opening and atom transfer radical polymerization produced model low dispersity materials comprising a single A = poly(lactide) (L) and multiple B = poly(dodecyl acrylate) (D) arms that amplify "conformational asymmetry" through two concerted effects: the mikto architecture and disparate block statistical segment lengths. Analyzing the self-assembly of LD2 and LD3 samples resulted in the discovery of two TCP phases, σ and A15, that remained stable to significantly higher A-block volume fractions as the number of B arms increased. These results experimentally establish the importance of conformational asymmetry and molecular architecture as powerful design tools for the self-assembly of block copolymers into nonclassical phases.

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.

Dynamics of a Supercooled Disordered Sphere-Forming Diblock Copolymer as Determined by X-ray Photon Correlation and Dynamic Mechanical Spectroscopies.

We report the dynamic behavior of a sphere-forming poly(styrene)-block-poly(1,4-butadiene) (PS-PB) diblock copolymer comprising 20 vol % PB below the order-disorder transition temperature (TODT = 153 °C) using dynamic mechanical spectroscopy (DMS) and X-ray photon correlation spectroscopy (XPCS). A time-temperature transformation diagram was constructed by monitoring the elasticity of the sample as a function of time following rapid quenches of the disordered melt to various temperatures T < TODT. Isothermal frequency spectra acquired prior to nucleation of the ordered BCC phase were time-temperature superposed, and the shift factors were fit using the Williams-Landel-Ferry (WLF) equation. For comparison, XPCS measurements were used to extract relaxation times from the supercooled liquid as a function of the quench temperature. Alignment of the temperature dependence of the XPCS-based relaxation times with that of the WLF shift factors in the range T = 125-140 °C indicates that both techniques probe the fluctuating mesomorphic micelle dynamics mediated by the relaxation modes of individual chains, including interparticle chain exchange. For deeper quench temperatures, TODT - T ≥ 28 °C, departure of the XPCS time constant from WLF behavior is consistent with a jamming transition, analogous to that encountered in concentrated colloidal systems. We postulate that the dominant relaxation mode in the supercooled disordered liquid transitions from ergodic dynamics governed by chain exchange to a nonergodic regime dominated by local rearrangement of micellar particles at T ≈ Terg, where Terg denotes the ergodicity temperature.