Monomer Fluctuations and the Distribution of Residual Bond Orientations in Polymer Networks

On the Swelling of Polymer Network Strands

Large scale computer simulations are employed to analyze the conformations of network strands in polymer networks at preparation conditions (characterized by a polymer volume fraction of ϕ0) and when swollen to equilibrium (characterized by a polymer volume fraction ϕ < ϕ0). Network strands in end-linked model networks are weakly stretched and partially swollen at preparation conditions as compared to linear polymers in the same solvent at ϕ0. Equilibrium swelling causes non-ideal chain conformations characterized by an effective scaling exponent approaching 7/10 on intermediate length scales for increasing overlap of the chains. The chain size in a network consists of a fluctuating and a time average "elastic" contribution. The elastic contribution swells essentially affinely ∝(ϕ0/ϕ)2/3, whereas the swelling of the fluctuating part lies between the expected swelling of the entanglement constraints and the swelling of non-cross-linked chains in a comparable semi-dilute solution. The total swelling of chain size results from the changes of both fluctuating and non-fluctuating contributions.

Auxetic polymer networks: The role of crosslinking, density, and disorder

Low-crosslinked polymer networks have recently been found to behave auxetically when subjected to small tensions, that is, their Poisson's ratio ν becomes negative. In addition, for specific state points, numerical simulations revealed that diamond-like networks reach the limit of mechanical stability, exhibiting values of ν = -1, a condition that we define as hyper-auxeticity. This behavior is interesting per se for its consequences in materials science but is also appealing for fundamental physics because the mechanical instability is accompanied by evidence of criticality. In this work, we deepen our understanding of this phenomenon by performing a large set of equilibrium and stress-strain simulations in combination with phenomenological elasticity theory. The two approaches are found to be in good agreement, confirming the above results. We also extend our investigations to disordered polymer networks and find that the hyper-auxetic behavior also holds in this case, still manifesting a similar critical-like behavior as in the diamond one. Finally, we highlight the role of the number density, which is found to be a relevant control parameter determining the elastic properties of the system. The validity of the results under disordered conditions paves the way for an experimental investigation of this phenomenon in real systems, such as hydrogels.

Introducing "MEW2" Software: A Tool to Analyze MQ-NMR Experiments for Elastomers

Low-field time-domain proton Nuclear Magnetic Resonance (NMR) spectroscopy is an attractive and powerful tool for studying the structure and dynamics of elastomers. The existence of crosslinks and other topological constraints in rubber matrices (entanglements and filler-rubber interactions, among others) renders the fast segmental fluctuations of the polymeric chains non-isotropic, obtaining nonzero residual dipolar couplings, which is the main observable of MQ-NMR experiments. A new software, Multiple quantum nuclear magnetic resonance analyzer for Elastomeric Networks v2 (MEW2), provides a new tool to facilitate the study of the molecular structure of elastomeric materials. This program quantitatively analyzes two different sets of experimental data obtained in the same experiment, which are dominated by multiple-quantum coherence and polymer dynamics. The proper quantification of non-coupled network defects (dangling chain ends, loops, etc.) allows the analyzer to normalize the multiple quantum intensity, obtaining a build-up curve that contains the structural information without any influence from the rubber dynamics. Finally, it provides the spatial distribution of crosslinks using a fast Tikhonov regularization process based on a statistical criterion. As a general trend, this study provides an automatic solution to a tedious procedure of analysis, demonstrating a new tool that accelerates the calculations of network structure using 1H MQ-NMR low-field time-domain experiments for elastomeric compounds.

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.

Structure and elasticity of model disordered, polydisperse, and defect-free polymer networks

The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly cross-linked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carried out, but that systems with the same mean valence and same assembly density have the same structural properties. Moreover, we compute the long-time limit of the mean-squared displacement, also known as the (squared) localization length, of the cross-links and of the middle monomers of the strands, showing that the dynamics of long strands is well described by the tube model. Finally, we find a relation connecting these two localization lengths at high density and connect the cross-link localization length to the shear modulus of the system.

Crosslinked Elastomers: Structure-Property Relationships and Stress-Optical Law

We present a combination of independent techniques in order to characterize crosslinked elastomers. We combine well-established macroscopic methods, such as rheological and mechanical experiments and equilibrium swelling measurements, a more advanced technique such as proton multiple-quantum NMR, and a new method to measure stress-induced segmental orientation by in situ tensile X-ray scattering. All of these techniques give access to the response of the elastomer network in relation to the crosslinking of the systems. Based on entropic elasticity theory, all these quantities are related to segmental orientation effects through the so-called stress-optical law. By means of the combination of these techniques, we investigate a set of unfilled sulfur-vulcanized styrene butadiene rubber elastomers with different levels of crosslinking. We validate that the results of all methods correlate very well. The relevance of this approach is that it can be applied in any elastomer materials, including materials representative of various industrial application, without prerequisite as regards, e.g., optical transparency or simplified formulation. Moreover, the approach may be used to study reinforcement effects in filled elastomers with nanoparticles.

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.

Glassy and Polymer Dynamics of Elastomers by 1H Field-Cycling NMR Relaxometry: Effects of Cross-Linking

¹H spin lattice relaxation rate (R₁) dispersions were acquired by field-cycling (FC) NMR relaxometry between 0.01 and 35 MHz over a wide temperature range on polyisoprene (IR), polybutadiene (BR), and poly(styrene-co-butadiene) (SBR) rubbers, obtained by vulcanization under different conditions, and on the corresponding uncured elastomers. By exploiting the frequency–temperature superposition principle, χ″(ωτ_s) master curves were constructed by shifting the total FC NMR susceptibility, χ″(ω) = ωR₁(ω), curves along the frequency axis by the correlation times for glassy dynamics, τ_s. Longer τ_s values and, correspondingly, higher glass transition temperatures were determined for the sulfur-cured elastomers with respect to the uncured ones, which increased by increasing the cross-link density, whereas no significant changes were found for fragility. The contribution of polymer dynamics, χ_pol^″(ω), to χ″(ω) was singled out by subtracting the contribution of glassy dynamics, χ_glass^″(ω), well represented using a Cole–Davidson spectral density. For all elastomers, χ_pol^″(ω) was found to represent a small fraction, on the order of 0.05–0.14, of the total χ″(ω), which did not show a significant dependence on cross-link density. In the investigated temperature and frequency ranges, polymer dynamics was found to encompass regimes I (Rouse dynamics) and II (constrained Rouse dynamics) of the tube reptation model for the uncured elastomers and only regime I for the vulcanized ones. This is clear evidence that chemical cross-links impose constraints on chain dynamics on a larger space and time scale than free Rouse modes.

Elasticity of Phantom Model Networks with Cyclic Defects

The impact of finite cycles on the phantom modulus in an otherwise perfect network is computed exactly. It is shown that pending cycles reduce the phantom modulus of the network by kT/V independent of junction functionality. The correction for nonpending cycles is larger than estimated previously within this particular approximation of the surrounding network structure. It is discussed that loop formation inevitably leads to streched chain conformations, if the loops are built step by step as part of the network structure. All network loops tend to contract simultaneously to optimize conformations, which leads to an increasing stretch of chains in larger loops that can be observed in computer simulations. Possible other corrections to the phantom modulus that were left aside in previous work are discussed briefly.

NEW INSIGHTS INTO RUBBER NETWORK STRUCTURE BY A COMBINATION OF EXPERIMENTAL TECHNIQUES

Robust quantitative cross-link density characterization becomes necessary for the complete understanding of the structure and optimization of final properties of rubber compounds for industrial applications. A combination of different experimental techniques have been used to establish the quantitative consistency on the correlations between the results obtained by the individual methods within a reliable unique (physically based) platform reclined on the concept of rubber elasticity that considers the impact of entanglements in technical rubbers. The contribution of cross-links and elastically active entanglements to mechanical properties has been quantified by the analysis of uniaxial stress–strain measurements by means of the extended tube model of rubber elasticity. In a complementary manner, rubber network structure has also been investigated by state-of-the-art multiple-quantum low-field NMR experiments and classical T1 and T2 relaxation measurements. In addition, equilibrium swelling data were analyzed by the classical phantom and Flory–Rehner limits as well as by applying the theoretical approach proposed by Helmis, Heinrich, and Straube that takes into account topological constraints during swelling. Correlations among these complementary techniques have been reported, and the interpretation of the obtained differences is addressed. The baseline study focuses on unfilled NR, setting the basis for the investigation of unfilled SBR matrices and filled rubbers.

The formation and structure of Olympic gels

Different methods for creating Olympic gels are analyzed using computer simulations. First ideal reference samples are obtained from freely interpenetrating semi-dilute solutions and melts of cyclic polymers. The distribution of pairwise concatenations per cyclic molecule is given by a Poisson-distribution and can be used to describe the elastic structure of the gels. Several batches of linear chains decorated with different selectively binding groups at their ends are mixed in the "DNA Origami" technique and network formation is realized. While the formation of cyclic molecules follows mean field predictions below overlap of the precursor molecules, an enhanced ring formation above overlap is found that is not explained by mean field arguments. The "progressive construction" method allows to create Olympic gels with a single reaction step from a concentrated mixture of large compressed rings with a low weight fraction of short chains that are below overlap concentration. This method, however, is limited by the difficulty to obtain a sufficiently high degree of polymerization of the large rings.

Conformations of a Long Polymer in a Melt of Shorter Chains: Generalizations of the Flory Theorem

Large-scale simulations of the swelling of a long N-mer in a melt of chemically identical P-mers are used to investigate a discrepancy between theory and experiments. Classical theory predicts an increase of probe chain size R ∼ P^-0.18 with decreasing degree of polymerization P of melt chains in the range of 1 < P < N^1/2. However, both experiment and simulation data are more consistent with an apparently slower swelling R ∼ P^-0.1 over a wider range of melt degrees of polymerization. This anomaly is explained by taking into account the recently discovered long-range bond correlations in polymer melts and corrections to excluded volume. We generalize the Flory theorem and demonstrate that it is in excellent agreement with experiments and simulations.