End-linked Networks Research Articles

Stress-Induced Orientation of Cocontinuous Nanostructures within Randomly End-Linked Copolymer Networks

Randomly end-linked copolymer networks (RECNs) provide a robust route to self-assembled cocontinuous nanostructures. Here, we study the orientation of cocontinuous polystyrene/poly(d,l-lactide) (PS/PLA) RECNs induced by uniaxial stretching above the glass transition temperatures of the components. Small-angle X-ray scattering (SAXS) reveals that the domains initially undergo nonaffine stretching at low strain (ε < 0.4), followed by domain rotation at larger strains, yielding a "soft elastic" response and providing a high degree of orientation. Transmission electron microscopy (TEM) tomography confirms that stretching leads to topological changes in the nanostructure, corresponding to reorganization of domain interfaces. The combination of orientation at the molecular and nanostructural levels provides substantial improvements in yield strength, toughness, and stiffness. In addition to possibilities for improving mechanical properties, cocontinuous nanostructures with controlled levels of orientation have potential in a variety of contexts including directional ion transport and energy absorption.

Counting Secondary Loops Is Required for Accurate Prediction of End-Linked Polymer Network Elasticity.

To predict and understand the properties of polymer networks, it is necessary to quantify network defects. Of the various possible network defects, loops are perhaps the most pervasive and yet difficult to directly measure. Network disassembly spectrometry (NDS) has previously enabled counting of the simplest loops-primary loops-but higher-order loops, e.g., secondary loops, have remained elusive. Here, we report that the introduction of a nondegradable tracer within the NDS framework enables the simultaneous measurement of primary and secondary loops in end-linked polymer networks for the first time. With this new "NDS2.0" method, the concentration dependences of the primary and secondary loop fractions are measured; the results agree well with a purely topological theory for network formation from phantom chains. In addition, semibatch monomer addition is shown to decrease both primary and secondary loops, though the latter to a much smaller extent. Finally, using the measured primary and secondary loop fractions, we were able to predict the shear storage modulus of end-linked polymer gels via real elastic network theory (RENT).

Molecular Dynamics Simulation Study of Polymer Nanocomposites with Controllable Dispersion of Spherical Nanoparticles.

Through coarse-grained molecular dynamics simulation, we construct a novel kind of end-linked polymer network by employing dual end-functionalized polymer chains that chemically attach to the surface of nanoparticles (NPs), so that the NPs act as large cross-linkers. We examine the effects of the length and flexibility of polymer chains on the dispersion of NPs, and the effect of the chain length on the stress-strain behavior and the segment orientation during the deformation process. We find that the stress upturn becomes more prominent with the decrease of the chain length, attributed to the limited extensibility of the chain strand connecting two neighboring NPs. In addition, this end-linked polymer nanocomposite (PNC) is shown to have a temperature-dependent stress-strain behavior that is contrary to traditional physically mixed PNCs, whose mechanical properties deteriorate with increasing temperature. This is due to the stability of the dispersion of NPs and higher entropic elasticity at higher temperature for the former, while the latter has poorer interfacial interaction at higher temperature, leading to less reinforcing efficiency. By imposing a dynamic oscillatory shear deformation, we obtain a dynamic hysteresis loop for end-linked and physically mixed dispersions. Interestingly, the end-linked system possesses a much smaller hysteresis loss than does the physically mixed system, with the latter exhibiting a more prominent decrease with increasing temperature, due to less interfacial contact. Our results demonstrate that end-linked PNCs combine attractive static and dynamic mechanical properties and exhibit an unusual response to temperature, which could find potential applications in the future.

Comprehensive study on temperature-induced crystallisation and strain-induced crystallisation behaviours of natural rubber/isoprene rubber blends

ABSTRACTThe temperature-induced crystallisation (TIC) and strain-induced crystallisation (SIC) of natural rubber (NR)/isoprene rubber (IR) blends varying in blend ratio were mainly studied by dilatometers and wide-angle X-ray diffraction measurements (WAXD). The dilatometers results showed that the real half-life of crystallisation (t1/2) values of unvulcanised NR/IR blends were 50% less than the theoretical half-life of crystallisation values. From WAXD measurements, the degree of crystallisation of vulcanised NR/IR with IR content samples 30, 50 and 70% at strain 500% were larger than theoretical crystallinity values by 17.17, 19.99 and 29.69%. NR can significantly improve the property of crystallinity of IR during TIC and SIC processes. The results can be ascribed to the end-linked networks existing in NR which can simultaneously induce amorphous NR and IR chains into crystalline order in NR/IR blends and increase the crystallinity and crystallisation rate during TIC and SIC process.

Anisotropic and Interconnected Nanoporous Materials from Randomly End-Linked Copolymer Networks

Microphase separation within randomly end-linked copolymer networks (RECNs) provides access to disordered bicontinuous morphologies over a wide composition range of the constituent network strands. Here, we rely on end-linking of telechelic hydroxyl-terminated polystyrene (PS) and poly(d,l-lactide) (PLA) chains of equal molecular weight, with a tetrafunctional isocyanate cross-linker in a good solvent for both strands, followed by solvent removal to induce microphase separation, and finally etching of the PLA phase to yield nanoporous materials. Transmission electron microscopy (TEM) tomographic reconstructed 3D images along with gravimetric measurements and small-angle X-ray scattering (SAXS) indicate the formation of highly interconnected structures over a range of ∼40–70 vol % of PLA, while N2 adsorption measurements indicate narrowly distributed pore sizes that can be tuned by varying the strand molecular weights. Stretching of the PS/PLA copolymer networks above the glass transition temperatures of b...

Relation between Cross-Link Fluctuations and Elasticity in Entangled Polymer Networks

Computer simulation data on junction fluctuations in end-linked model networks are analyzed using the framework of the constraint junction model and the slip tube model for entangled networks. It is argued that cross-linking freezes in conformational fluctuations of chains and cross-links, which creates a small preload of entangled strands. This can be modeled using a “confinement degree of polymerization” Nc(N) with a weak dependence on the degree of polymerization N. The confined motion of network junctions with f active connections to the network is well described by using the exact solution of the constrained junction model with a constraining term that is given by the superposition of f/2 entanglement tubes with confinement Nc(N). It is shown that the modulus of end-linked model networks is the sum of a phantom and an entanglement contribution, whereby the entanglement contribution shows the same correction Nc(N) as both the cross-link fluctuations and the time average bond orientations. The results ...

Odd–Even Effect of Junction Functionality on the Topology and Elasticity of Polymer Networks

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...

Engineering the Dynamic Properties of Protein Networks through Sequence Variation.

The dynamic behavior of macromolecular networks dominates the mechanical properties of soft materials and influences biological processes at multiple length scales. In hydrogels prepared from self-assembling artificial proteins, stress relaxation and energy dissipation arise from the transient character of physical network junctions. Here we show that subtle changes in sequence can be used to program the relaxation behavior of end-linked networks of engineered coiled-coil proteins. Single-site substitutions in the coiled-coil domains caused shifts in relaxation time over 5 orders of magnitude as demonstrated by dynamic oscillatory shear rheometry and stress relaxation measurements. Networks with multiple relaxation time scales were also engineered. This work demonstrates how time-dependent mechanical responses of macromolecular materials can be encoded in genetic information.

Subnanoscopic inhomogeneities in model end-linked PDMS networks probed by positron annihilation lifetime spectroscopy and their effects on thermomechanical properties

The subnanoscopic free volume hole properties of model poly(dimethylsiloxane) (PDMS) networks with unimodal and bimodal distribution of chain lengths between the cross-links were determined using positron annihilation life time spectroscopy (PALS). Wide angle X-ray diffraction (WAXD) and small angle X-ray scattering (SAXS) studies were carried out to further understand the structural inhomogeneities of the networks at different length scales. The networks were prepared by end-linking combinations of sufficiently longer (Mn = 18,952) and shorter (Mn = 4323) precursor PDMS chains relative to entanglement spacing (Me). The macroscopic properties of the networks were studied by tensile testing, dynamic mechanical analysis (DMA), differential scanning calorimetry (DSC), as well as equilibrium swelling measurements. Through PALS studies it was possible to delineate the subtle variations in the elementary mesh sizes, a measure of the segmental spacing, of the unimodal short and long chain networks influenced by cross-links or entanglements. The intersegmental spacing of the unimodal PDMS networks at a length scale of few angstroms obtained from WAXD measurements were found to be almost in quantitative agreement with the free volume hole sizes obtained from PALS. SAXS measurements on solvent swollen PDMS networks from short and long chain precursors were used to obtain correlation length of the networks at a higher length scale of a few nanometers. Further, the studies revealed that the enhanced mechanical properties seen in certain bimodal elastomer networks are connected with topological features of the networks. A noteworthy finding from PALS studies was that the bimodal composition with 20 wt% short chain, which showed the best combination of mechanical properties with a feature of stress-upturn in tensile testing, exhibited the least free volume size and relatively lower dispersion in its size distribution among the networks. These fundamental studies are expected to provide new insights into the network structure of model elastomers at a molecular scale and its possible connection with macroscopic properties.

Contribution of Linear Guest and Structural Pendant Chains to Relaxational Dynamics in Model Polymer Networks Probed by Time-Domain 1H NMR

A series of end-linked polymer networks with varying contents of linear guest chains were investigated through swelling and time-domain NMR temperature dependent experiments. Taking advantage of the thermorheological simplicity of polydimethylsiloxane polymers, time–temperature superposition (TTS) was employed to expand the characteristic time scales of NMR exploration by about 2 orders of magnitude. A comparison between swelling data and tube model predictions reveals that NMR captures the dominant features of the equilibrium and dynamic properties of defects trapped in slightly cross-linked, entanglement-dominated polymer networks. As high-temperature experiments ensures a complete relaxation of the guest linear chains on the millisecond time scale of the NMR experiments, an accurate description of the network architecture can be provided. Contents of guest chains determined by NMR were found to agree within a 1 wt % accuracy with data of swelling experiments.

Structural and mechanical properties of advanced polymer gels with rigid side-chains using coarse-grained molecular dynamics

Computational modeling was utilized to design complex polymer networks and gels which display enhanced and tunable mechanical properties. Our approach focuses on overcoming traditional design limitations often encountered in the formulation of simple, single polymer networks. Here, we use a coarse-grained model to study an end-linked flexible polymer network diluted with branched polymer solvent chains, where the latter chains are composed of rigid side-chains or “spikes” attached to a flexible backbone. In order to reduce the entropy penalty of the flexible polymer chains these rigid “spikes” will aggregate into clusters, but the extent of aggregation was shown to depend on the size and distribution of the rigid side-chains. When the “spikes” are short, we observe a lower degree of aggregation, while long “spikes” will aggregate to form an additional secondary network. As a result, the tensile relaxation modulus of the latter system is considerably greater than the modulus of conventional gels and is approximately constant, forming an equilibrium zone for a broad range of time. In this system, the attached long “spikes” create a continuous phase that contributes to a simultaneous increase in tensile stress, relaxation modulus and fracture resistance. Elastic properties and deformation mechanisms of these branched polymers were also studied under tensile deformation at various strain rates. Through this study we show that the architecture of this branched polymer can be optimized and thus the elastic properties of these advanced polymer networks can be tuned for specific applications.

Confined crystallization in end-linked PEO network under uniaxial extension

In this work extension induced crystallization of end-linked polyethylene oxide (PEO) network was investigated with in-situ small angle X-ray scattering (SAXS) and rheological measurement. The coupling between crystallinity and stress of crosslinked network makes the morphology time dependent. With a large strain the structure evolution in the stretched network is found to follow a two-stage process: i) crystals with high numerical density and small dimension form first, which laterally correlate with adjacent ones; ii) continuous melting and fusing of adjacent crystal happen after the first nucleation stage, leading to increase of crystal dimension and stability. Decreasing strain a gradual transformation to normal lamellae formation is found. Strain tuned confinement and crystallization induced confinement release is supposed to induce the structural change.

Molecular dynamics simulation of O2 diffusion in polydimethylsiloxane (PDMS) and end-linked PDMS networks

Molecular dynamics simulations are used to compute diffusion coefficients for O2 molecules in polydimethylsiloxane (PDMS) and end-linked PDMS networks. The PDMS chains and penetrants are modelled using a hybrid interatomic potential which treats the Si and O atoms along the chain backbone explicitly while coarse-graining the methyl side groups and penetrants. In PDMS models with different molecular weights, diffusivity of the O2 penetrants is found to modestly decrease with an increase in chain length. To match typical experimental conditions, the end-linked PDMS networks are constructed with a PDMS to crosslinking (CL) molecule mass ratio of 5:1 or 10:1, demanding that the number of CL molecules exceeds the number of PDMS chains in each model. Despite end-linking, the presence of non-bonded CL molecules promotes increased O2 diffusivity in comparison with uncrosslinked PDMS. Temperature dependence is captured using the Williams–Landel–Ferry equation.

Entanglements and Networks to Strain-Induced Crystallization and Stress–Strain Relations in Natural Rubber and Synthetic Polyisoprene at Various Temperatures

Stress–strain relations and strain-induced crystallization (SIC) of unvulcanized and vulcanized states of natural rubber (NR) and synthetic polyisoprene (IR) were studied using synchrotron X-ray at various temperatures from −50 to +75 °C. Unvulcanized IR is a polymer melt that shows a viscous response with yield stress that is related to entanglement and no SIC at 25 °C. However, unvulcanized IR shows SIC at 0, −25, and −50 °C. Entanglements in unvulcanized IR become pivots to align chains and induce crystals at low temperatures. On the other hand, unvulcanized NR shows SIC and stress upturns in stress–strain relations at 25 °C. Since a permanent set is observed after large extension and retraction, unvulcanized NR has a pseudo end-linked network. The pseudo end-linked networks make entanglements as permanent entanglements and show stress upturn and SIC. Vulcanization makes IR to a rubber which shows a stress upturn and SIC by chemical bond network. The stress of vulcanized NR and IR appear almost the same at strains less than 3.0, however the stress of vulcanized NR is much higher than vulcanized IR beyond strain 3.0. The onset strain of SIC of vulcanized NR is much smaller than vulcanized IR. This different behavior is caused by the pseudo end-linked network. The stress in stress–strain relation at higher temperatures is significantly lower than the stress at lower temperatures. This tendency does not seem to follow the theory of rubber elasticity. The onset of SIC delays the upturn of stress as a shoulder or plateau in the stress–strain relation. SIC contributes to the stress, even though the stress smoothly increases with strain. At higher strain, SIC become big network points to bind many chains and reduce the limit of extensibility. The effect of SIC and the limited extensibility to the stress is not distinguishable.

Mechanical and Swelling Behaviors of End-Linked PDMS Rubber and Randomly Cross-Linked Polyisoprene

In the present work, we report the results of an investigation of the temperature and cross-link density dependences of the swelling activity parameter S, or dilational modulus, which represents a difference in free energy between the cross-linked and the uncross-linked systems, for PDMS and polyisoprene within the framework of the Frenkel–Flory–Rehner (FFR) theory. We find that the values of S (λ2 → 1), where λ is the swelling stretch, are nonzero and increase as the cross-linking density increases, implying that the Flory–Huggins interaction parameters, which represents the energy contribution from interspersing polymer and solvent molecules, of the cross-linked (χc) and uncross-linked (χu) systems are different. The full analysis of S vs λs2 within the FFR model also leads to the new result that the difference between χc and χu decreases as the degree of swelling increases. Results from torsional measurements for network elasticity determination of the PDMS end-linked networks are also presented.

Counting primary loops in polymer gels

Much of our fundamental knowledge related to polymer networks is built on an assumption of ideal end-linked network structure. Real networks invariably possess topological imperfections that negatively affect mechanical properties; modifications of classical network theories have been developed to account for these defects. Despite decades of effort, there are no known experimental protocols for precise quantification of even the simplest topological network imperfections: primary loops. Here we present a simple conceptual framework that enables primary loop quantification in polymeric materials. We apply this framework to measure the fraction of primary loop junctions in trifunctional PEG-based hydrogels. We anticipate that the concepts described here will open new avenues of theoretical and experimental research related to polymer network structure.

Impact of precursor size on the chain structure and mechanical properties of solvent-swollen epoxy gels

The thermal and mechanical properties of solvent-swollen epoxy gels were investigated as a function of pre-cursor size in a model end-linked network. The epoxy networks were formed by cross-linking diepoxide and diamine precursors in the presence of a low volatility solvent, dibutylphthalate (DBP). Both precursors were end functionalized and contained a poly(propylene glycol) (PPG) spacer between the epoxy and amine functionality, respectively. The lengths of both precursors were controlled by varying the molecular weight of the PPG spacer between functional groups. The glass transition temperature for the gels as a function of solvent loading was well predicted by the Fox equation. The scaling factors of shear storage modulus versus solvent loading increased with increasing diamine precursor molecular weight to values much larger (3.91) than the theoretical value of 2.3, for entanglement dominated network formation in a theta solvent. In contrast, the scaling factor increased with decreasing epoxy precursor molecular weight to values near 4.5. The large, molecular weight dependent scaling factors are attributed to loop defect formation as the result of the amine cross-linker architecture, which consists of two difunctional reactive end groups separated by a spacer. Rather than equal spacing of all four reactive sites, the amine end groups contain two reactive hydrogens that increase the local concentration of reactive species, and facilitates loop formation. We anticipate that this work will aid in the development of non-aqueous gels and provide enhanced tailoring of the gel properties over a broad range of stiffness.

Effect of Precursor Molar Mass on the 2H NMR Line Shapes of End-Linked PDMS Elastomers

A series of end-linked PDMS networks synthesized with different molar mass precursor chains is examined using 2H NMR spectroscopy. The resulting line shapes for networks in the undeformed state show clear differences with precursor chain molar mass. Furthermore, samples uniaxially extended to high extension ratio show a clear shoulder in the line shape and two characteristic splittings (two doublets). Comparison with spectra for deuterated free chains dissolved in an unlabeled network confirms that the inner doublet results from excluded volume interactions between segments whereas the outer doublet is due to more highly aligned chain segments from chains with conformations trapped by the cross-linking reaction.

PLGA−POSS End-Linked Networks with Tailored Degradation and Shape Memory Behavior

Biodegradable PLGA oligomers were synthesized to feature a hybrid organic−inorganic moiety, POSS, incorporated at the center of each chain by using it as the ring-opening initiator. After end-capping with vinyl groups, the macromers were photocured into networks with POSS content ranging from 10 to 41 wt %. Increasing POSS inclusion increased the crystallinity of the network while decreasing the degradation rate due to its hydrophobic and nonhydrolyzable properties. It was found that co-curing PLGA oligomers with and without POSS in the backbone could be utilized to create networks with a reduced POSS loading level, at a given cross-link density, allowing tuned crystallinity. Hydrolytic degradation of the co-cured networks was slower than for the PLGA homonetwork but still led to complete degradation after 14 weeks in PBS buffer at 37 °C. The networks exhibited versatile shape memory properties, exploiting the combination of covalent cross-linking and the glass transition, POSS-phase melting temperature, ...

Diffusion in Model Networks as Studied by NMR and Fluorescence Correlation Spectroscopy

We have studied the diffusion of small solvent molecules (octane) and larger hydrophobic dye probes in octane-swollen poly(dimethyl siloxane) linear-chain solutions and end-linked model networks, using pulsed-gradient nuclear magnetic resonance (NMR) and fluorescence correlation spectroscopy (FCS), respectively, focusing on diffusion in the bulk polymer up to the equilibrium degree of swelling of the networks, that is, 4.8 at most. The combination of these results allows for new conclusions on the feasibility of different theories describing probe diffusion in concentrated polymer systems. While octane diffusion shows no cross-link dependence, the larger dyes are increasingly restricted by fixed chemical meshes. The simple Fujita free-volume theory proved most feasible to describe probe diffusion in linear long-chain solutions with realistic parameters, while better fits were obtained assuming a stretched exponential dependence on concentration. Importantly, we have analyzed the cross-link specific effect on probe diffusion independently of any specific model by comparing the best-fit interpolation of the solution data with the diffusion in the networks. The most reasonable description is obtained by assuming that the cross-link effect is additive in the effective friction coefficient of the probes. The concentration dependences as well as the data compared at the equilibrium degrees of swelling indicate that swelling heterogeneities and diffusant shape have a substantial influence on small-molecule diffusion in networks.