End-linked Networks Research Articles

Interconnected Nanoporous Polysulfone by the Self-Assembly of Randomly Linked Copolymer Networks and Linear Multiblocks.

Porous materials have attracted considerable attention due to their versatile applications, especially in water purification. Interconnected nanoporous structures are distinguished by their high degree of porosity and resistance to clogging, as well as their insensitivity to nanostructural orientation. Previous works on randomly linked copolymer systems have shown that they can effectively produce disordered cocontinuous nanostructures, which upon removal of one component yield interconnected nanoporous materials. However, the cocontinuous nanomaterials previously developed using polystyrene (PS) and poly(d,l-lactic acid) (PLA) strands, and the resulting interconnected nanoporous PS monoliths, were far too brittle to enable practical use as membranes. Here, we study the self-assembly of randomly linked copolymer networks prepared using blocks of the engineering polymer polysulfone (PSU). A wide cocontinuous regime (spanning 40 wt %) was found for randomly end-linked copolymer networks (RECNs) constructed from PSU and PLA strands, via a combination of mechanical testing, gravimetry, small-angle X-ray scattering, and scanning electron microscopy. The PSU/PLA cocontinuous nanomaterial with symmetric composition showed 2.4 times higher Young's modulus and ∼100 times greater toughness than the corresponding PS/PLA sample. The interconnected nanoporous PSU fabricated after etching of PLA even exhibited 1.6 times greater toughness than PS/PLA prior to PLA removal. To facilitate the production of thin films of cocontinuous nanomaterials, we applied solution-processable randomly linked linear PSU/PLA multiblock polymers onto ultrafiltration membranes. The interconnected nanoporous PSU thin film generated by etching PLA was found to effectively reject 50 nm diameter particles without significantly compromising permeability. This discovery presents a valuable addition to the existing techniques used to fabricate PSU membranes. In contrast to traditional methods, which are sensitive to processing conditions, produce a wide range of pore sizes, and offer limited adjustability of pore size, the current technique is anticipated to enable interconnected PSU membranes with more uniform and tailorable porosity.

A Comparison between Predictions of the Miller-Macosko Theory, Estimates from Molecular Dynamics Simulations, and Long-Standing Experimental Data of the Shear Modulus of End-Linked Polymer Networks.

Long-standing experimental data on the elastic modulus of end-linked poly(dimethylsiloxane) (PDMS) networks are employed to corroborate the validity of the Miller-Macosko theory (MMT). The validity of MMT is also confirmed by molecular dynamics (MD) simulations that mimic the experimentally realized networks. It becomes apparent that for a network formed from bulk, where the fractions of the loops are small, it is sufficient to account for the topological details of a reference tree-like network, i.e., for its degree of completion, junction functionalities, and trapped entanglements, in order to practically predict the modulus. However, a mismatch is identified between the MMT and MD simulations in relating the fraction of the soluble material to the extent of reaction. A large contribution of entanglements to the modulus of PDMS networks prepared with short precursor chains is presented, suggesting that the elastic modulus of commonly used end-linked PDMS networks is in fact entanglement-dominated.

Predicting failure locations in model end-linked polymer networks

Predicting failure locations in model end-linked 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-fluctuatingcontributions.

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.

Kinetic Model for Off-Stoichiometric Cross-Linking Reactions of End-Linked Polymer Networks

Kinetic Model for Off-Stoichiometric Cross-Linking Reactions of End-Linked Polymer Networks

Cocontinuous Nanostructures by Microphase Separation of Statistically Cross-Linked Polystyrene/Poly(2-vinylpyridine) Networks.

Cocontinuous polymeric nanostructures have drawn considerable attention due to their ability to combine distinct, percolation-dependent properties of two different polymer domains. Randomly end-linked copolymer networks (RECNs) have previously been shown to support the formation of disordered cocontinuous nanostructures across wide composition windows in a robust way. However, achieving highly efficient linking of telechelic polymers with excellent end-group fidelity often requires complex synthetic routes. As an alternative, we study here statistically cross-linked copolymer networks (SCCNs) composed of polystyrene and poly(2-vinylpyridine) (PS and P2VP) with cross-linkable allyl pendent groups that are conveniently synthesized by controlled radical copolymerization. Via selective extraction of P2VP, coupled with gravimetry, small-angle X-ray scattering, and electron microscopy, we find disordered cocontinuous phases across wide composition ranges (up to ≈ 35 wt %), approaching values previously determined for RECNs. Remarkably, even for samples that appear to exhibit full percolation, a substantial fraction of P2VP (≈ 20-30 wt %) cannot be removed, which we ascribe to short strands between nearby cross-linkers that are physically embedded within PS domains. The resulting PS porous monoliths with residual surface P2VP layers enable facile surface modification to resist protein adsorption and templating of porous gold nanostructures.

Tunable mechanical properties of vulcanised styrene-butadiene rubber by regulating cross-linked molecular network structures

ABSTRACT Establishing the relationship between molecular structures and mechanical properties is of great significance for the structural design of vulcanised styrene-butadiene rubber (SBR). The molecular dynamics method was used to study the mechanical properties of cross-linked SBR with controlled network topology, and the corresponding molecular mechanism was analysed by the energy contribution during the stretching process. The results showed that the tensile stress of the end-linked network sample could be up to 20 times higher than that of the sample with dangling chains at an engineering strain of 1.4. Moreover, under the same fixed cross-linking degree, the tensile stress of the long-chain network sample was significantly higher than that of the short-chain network sample. This is because the molecular chains located in the main chain network will be highly oriented during the stretching process, while the proportion of highly oriented molecular chains is high in samples with end-linked networks or a large proportion of long chains. In addition, due to the limited relaxation of structural units, the end-linked network structure has good thermal stability.

Ring-Filling Effect on Stress–Strain Curves of Randomly End-Linked Tetra-Arm Prepolymers

To clarify the stress–strain relation of polymer networks filled with ring polymers, we investigated randomly end-linked networks produced by a pseudo-crosslinking process of tetra-arm prepolymers through coarse-grained molecular dynamics simulations of the Kremer–Grest model. We considered three types of systems: (1) randomly end-linked network without rings, (2) randomly end-linked network with superimposed rings, and (3) randomly end-linked network made from a blend of rings and tetra-arm prepolymers. First, the properties of the network structure (without rings) were investigated, revealing that the prepolymer concentrations affect the entanglement properties of networks. Next, we investigated the effect of rings on the networks because the ring polymers do not form bonds with the network but introduce topological constraints by chain penetration through rings. To characterize the chain penetration, we developed a novel method combining the chain shrinking process and the classification of the ring shape. The shape of the ring with multiple chain penetration was significantly altered by uniaxial stretching. We confirmed that rings with multiple chain penetrations enhanced or reduced the stress in the stress–strain curve depending on the underlying network structures and rings with or without penetrations of strands. These findings contribute to the material design of crosslinked rubbers filled with rings to control mechanical properties.

Fracture of model end-linked networks.

Advances in polymer chemistry over the last decade have enabled the synthesis of molecularly precise polymer networks that exhibit homogeneous structure. These precise polymer gels create the opportunity to establish true multiscale, molecular to macroscopic, relationships that define their elastic and failure properties. In this work, a theory of network fracture that accounts for loop defects is developed by drawing on recent advances in network elasticity. This loop-modified Lake-Thomas theory is tested against both molecular dynamics (MD) simulations and experimental fracture measurements on model gels, and good agreement between theory, which does not use an enhancement factor, and measurement is observed. Insight into the local and global contributions to energy dissipated during network failure and their relation to the bond dissociation energy is also provided. These findings enable a priori estimates of fracture energy in swollen gels where chain scission becomes an important failure mechanism.

Bimodal Polymer End-Linked Nanoparticle Network Design Strategy to Manipulate the Structure-Mechanics Relation.

A kind of bimodal polymer end-linked network employing nanoparticles (NPs) as net points has been designed and constructed through coarse-grained molecular dynamics simulation. We systematically explore the effects of the molecular weight (length of the long polymer chains), chain flexibility, and temperature on the accurate distribution of the spherical NPs and the resulting mechanical properties of the bimodal network. It is found that the NPs can be dispersed well, and a larger average distance between the NPs is realized with the increase of the length of the long polymer chains, the rigidity of short and long chains, and the temperature. There is a linear relationship between the average interparticle distance of NPs and the arithmetical average of the root-mean-square end-to-end distance of long and short chains. By adopting the uniaxial deformation, the stress-strain behavior and the bond orientation are examined. The results illustrate that introducing the short chains into the uniform long chains network can notably improve the tensile stress-strain performance. The bond orientation behaviors present that short chains are more prone to be oriented and stretched, contributing to more stress during the stretching process. Furthermore, enhanced stress-strain behaviors can be observed by manipulating the chain stiffness and temperature. Interestingly, the bimodal end-linked network reveals a distinctively enhanced stress-strain behavior versus the temperature, which is opposite to that of traditional physically mixed polymer nanocomposites (PNCs), attributed to a higher entropic elasticity and the uniform dispersion of NPs of the end-linked system at high temperatures. The network exhibits a linear relationship for the stress at a fixed strain versus the temperature. Notably, it is indicated that the contribution of entropy accounts for most of the total stress, while the change of internal energy only accounts for a small part, which is consistent with the experimental observation of the classic rubber elastic theory. In general, our study demonstrates a rational route to precisely control the spatial dispersion of the NPs and effectively tailor the mechanical properties of PNCs.

Monte Carlo Evidence on Simple Conventional Means to Characterize the Final Extent of Reaction of Cured End-Linked Polymer Networks through the Miller–Macosko Nonlinear Polymerization Theory

Polymer networks produced by hydrosilylation reaction between vinyl-terminated bifunctional precursor chains and f-functional cross-linkers, one of the most well-investigated end-linked polymers, h...

Comparative Experimental and Molecular Simulation Study of the Entropic Viscoelasticity of End-Linked Polymer Networks

Bifunctional vinyl-terminated poly(dimethylsiloxane) chains are end-linked by tetrafunctional tetrakis(dimethylsiloxy)silane cross-linkers to produce irregular polymer networks with controlled stoi...

Nanoparticle Mobility within Permanently Cross-Linked Polymer Networks

Coarse-grained molecular dynamics simulations were performed to investigate the mobility of nanoparticles (NPs) embedded in end-linked polymer networks, considering both the entangled and unentangl...

Analysis of the Gel Point of Polymer Model Networks by Computer Simulations

The gel point of end-linked model networks is determined from computer simulation data. It is shown that the difference between the true gel point conversion, pc, and the ideal mean field prediction for the gel point, pc,id, is a function of the average number of cross-links per pervaded volume of a network strand, P, and thus, exhibits an explicit dependence on junction functionality, f. In contrast, the amount of intramolecular reactions at the gel point is independent of f in a first approximation and exhibits a different power-law dependence on the overlap number of elastic strands as compared to the gel point delay, pc – pc,id. Therefore, pc – pc,id cannot be predicted from intramolecular reactions and vice versa in contrast to a long standing proposal in the literature. Instead, the main contribution to pc – pc,id for P > 1 arises from the extra bonds needed to bridge the gaps between giant molecules separated in space and scales roughly ∝ (P – 1)−1/2. Further corrections to scaling are due to nonideal reaction kinetics, composition fluctuations, and incompletely screened excluded volume, which are discussed briefly.

Molecular Dynamics Validation and Applications of the Maximum Entropy Homogenization Procedure for Predicting the Elastic Properties of Gaussian Polymer Networks

Molecular dynamics (MD) simulations are used to obtain direct estimates of the equilibrium shear modulus of 3D periodic microstructures of ideal end-linked Gaussian polymer networks. The same micro...

On the Elasticity of Polymer Model Networks Containing Finite Loops

Based upon the resistor analogy and using the ideal loop gas approximation(ILGA) it is shown that only pending loops reduce the modulus of an otherwise perfect network made of monodisperse strands and junctions of identical functionality. Thus, the cycle rank of the network with pending structures removed (cyclic and branched) is sufficient to characterize modulus, if the resistor analogy can be employed. It is further shown that it is impossible to incorporate finite cycles into a polymer network such that individual network strands are at equilibrium conformations while maintaining simultaneously a force balance at the junctions. Therefore, the resistor analogy provides only an approximation for the phantom modulus of networks containing finite loops. Improved approaches to phantom modulus can be constructed from considering a force balance at the junctions, which requires knowledge of the distribution of cross-link fluctuations in imperfect networks. Assuming loops with equilibrium conformations and a force balance at all loop junctions, a lower bound estimate for the phantom modulus, $G_{\text{ph}}\approx\left(\xi-c_{\text{f}}L_{1}\right)kT/V$ is obtained within the ILGA for end-linked model networks and in the limit of $L_{1}\ll\xi$. Here, $L_{1}$ is the number of primary ("pending") loops, $\xi$ the cycle rank of the network, $k$ the Boltzmann constant, $V$ the volume of the sample, and $T$ the absolute temperature. $c_{\text{f}}$ is a functionality dependent coefficient that is $\approx2.56$ for junction functionality $f=3$ and $\approx3.06$ for $f=4$, while it converges quickly towards $\approx4.2$ in the limit of large $f$. Further corrections to phantom modulus beyond finite loops are addressed briefly.

Microscopic State of Polymer Network Chains upon Swelling and Deformation

We use low-resolution proton NMR to probe the chain deformation in swollen and nonlinearly deformed vulcanized rubber and end-linked PDMS networks on a microscopic level, extending earlier work focusing on uniaxial stretching and isotropic dilation upon swelling toward biaxial deformation and deformation of swollen samples. Previous studies have revealed that chain deformation in bulk samples is best described by tube models, and that chains in swollen samples deform affinely after an initial desinterspersion stage, upon which entanglement-related packing effects are relieved. We test whether a subsequent deformation may also be closer to affine, and find that this is not the case. Unexpectedly, nonisotropic deformation of swollen samples also follows tube-model predictions, which is explained by a dominance of structural inhomogeneities and significant reorganization of the topological constraints active in the swollen and possibly even the bulk state.

Effects of Randomly End-Linked Copolymer Network Parameters on the Formation of Disordered Cocontinuous Phases

Randomly end-linked copolymer networks (RECNs) provide a robust route to cocontinuous nanoscale structures, yielding opportunities to integrate desirable and distinct properties of the constituent ...

Nonideality in Silicone Network Formation via Solvent Swelling and 1H Double-Quantum NMR

The versatile cross-linking chemistry of poly(dimethylsiloxane) (PDMS)-based materials affords a large research space in which polymers with widely varying elastomeric properties may be synthesized. Parameters such as chain length, cross-link density, cross-link functionality, filler content, and chain chemistry can all be modified to produce materials with specific physical and mechanical properties. Commercial polysiloxane-based, “silicone” elastomers are generally intractable, which makes the precise characterization of their networks problematic. We report here the application of equilibrium solvent uptake analysis and 1H double-quantum nuclear magnetic resonance (1H DQ NMR) spectroscopy to determine the network topology of end-linked PDMS networks with nonideal network topology. Despite their structural complexity, we can quantify both the classical and nonclassical contributions to network structure using 1H DQ NMR which are in reasonable agreement with solvent uptake data. These findings serve as the foundation for future investigations of even more complex commercial silicones using 1H DQ NMR.