Swelling behavior and mechanical properties of endlinked poly (dimethylsiloxane) networks and randomly crosslinked polyisoprene networks

Measurements of the equilibrium degree of swelling and of the equilibrium modulus were performed on poly(dimethylsiloxane) networks (PDMS) and on polyisoprene vulcanizates. The results support the concept that topological interactions between network chains, e.g. entanglements or the like, have a large influence on the rubber elastic behavior, at least within a certain range of network densities.PDMS networks having network chains of different lengths and varying functionlities of the crosslinks were prepared in bulk by endlinking fractionated ,-divinyl PDMS via multifunctional hydrogen-siloxanes (f=3 to 22). Natural rubber (NR) and synthetic liquid polyisoprene (IR) were cured in bulk with various amounts of dicumyl peroxide to give randomly crosslinked samples.The experimentally determined moduli and degrees of swelling were compared with theoretical predictions based on the phantom network theory and affine network theory, taking into account only chemical crosslinks. The observed discrepancies can be traced back to a contribution of topological interactions (trapped entanglements) to the total effective network density. The modulus and swelling data are consistent, thus ruling out non-equilibrium effects.     

Identifying the primitive path mesh in entangled polymer liquids

Similar to entangled ropes, polymer chains cannot slide through each other. These topological constraints, the so-called entanglements, dominate the viscoelastic behavior of high-molecular-weight polymeric liquids. Tube models of polymer dynamics and rheology are based on the idea that entanglements confine a chain to small fluctuations around a primitive path which follows the coarse-grained chain contour. To establish the microscopic foundation for these highly successful phenomenological models, we have recently introduced a method for identifying the primitive path mesh that characterizes the microscopic topological state of computer-generated conformations of long-chain polymer melts and solutions. Here we give a more detailed account of the algorithm and discuss several key aspects of the analysis that are pertinent for its successful use in analyzing the topology of the polymer configurations. We also present a slight modification of the algorithm that preserves the previously neglected self-entanglements and allows us to distinguish between local self-knots and entanglements between distant sections of the same chain. Our results indicate that the latter make a negligible contribution to the tube and that the contour length between local self-knots, N_lk is significantly larger than the entanglement length N_e. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 917–933, 2005     

Entanglement effects in model polymer networks

Many fundamental questions for the understanding of polymer networks are more suitably addressed by current computer simulations than by experiments. Details of the microscopic topology, such as the elastically active cluster or loop entanglements, can be identified as well as controlled. In particular, it is possible to isolate and quantify their effects on macroscopic observables such as the elastic modulus. The constraints due to connectivity and conserved topology are more clearly present for networks than for melts. Already for strand lengths between crosslinks which are relatively short, the effect of the conserved topology is important. The mode relaxation in a network is significantly different from that of a melt. For weakly crosslinked systems the melt entanglement length is the relevant scaling parameter. The elastic modulus of a long chain network under ideal conditions reaches an asymptotic value which is about 2.2 times smaller than the prediction of an affine model for a network made of strands of the melt entanglement length. An analysis of the stress reveals that in the linear regime the contribution from the excluded volume is dominant compared to that from the connectivity along the strands. For larger elongations, however, the non-linear elastic response is dominated by the chemically and topologically shortest paths through the system, where chemical crosslinks and topological entanglements between meshes of the network play a similarly important role.     

Intra- and inter-chain fluctuations in entangled polymer melts in bulk and confined to pore channels

It is known that topological restraints by “chain entanglements” severely affect chain dynamics in polymer melts. In this field-cycling NMR relaxometry and fringe-field NMR diffusometry study, melts of linear polymers in bulk and confined to pores in a solid matrix are compared. The diameter of the pore channels was 10 nm. It is shown that the dynamics of chains in bulk dramatically deviate from those observed under pore constraints. In the latter case, one of the most indicative signatures of the reptation model is verified 28 years after its prediction by de Gennes: The frequency and molecular mass dependencies of the spin-lattice relaxation time obey the power law T_! ∝ M⁰ v^3/4 on a time scale shorter than the longest Rouse relaxation time τ_R. The mean squared segment displacement in the pores was also found to be compatible to the reptation law < r²>∝ M^−1/2t^1/2 predicted for τ_R < t < τ_d, where τ_d is the so-called disengagement time. Contrary to these findings, bulk melts of entangled polymers show frequency and molecular mass dependencies significantly different from what one expects on the basis of the reptation model. The data can however be described with the aid of the renormalized Rouse theory.     

Molecular architecture and rheological characterization of novel intramolecularly crosslinked polystyrene nanoparticles

Novel polystyrene nanoparticles were synthesized by the controlled intramolecular crosslinking of linear polymer chains to produce well‐defined single‐molecule nanoparticles of varying molecular mass, corresponding directly to the original linear precursor chain. These nanoparticles are ideal to study the relaxation dynamics/processes of high molecular mass polymer melts, as the high degree of intramolecular crosslinking potentially inhibits entanglements. Both the nanoparticles and their linear analogs were characterized by measuring their intrinsic viscosity, hydrodynamic radius (R_h), and radius of gyration (R_g). The ratio R_g/R_h was computed to characterize the molecular architecture of the nanoparticles in solution, revealing a shift toward the constant density sphere limit with increasing crosslink density and molecular mass. Further, confirming particulate behavior, Kratky plots obtained from neutron scattering data show a shift toward particle‐like nature. The rheological behavior of the particles was found to be strongly dependent on both the extent of intramolecular crosslinking and molecular mass, with a minimal viscosity change at low crosslinking levels and a gel‐like behavior evident for a large degree of crosslinking. These and other results suggest the presence of a secondary mode of polymer relaxation/movement besides reptation, which in this case, is influenced by the total number of crosslinked loops present in the nanoparticle. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1930–1947, 2006     

Effect of the topology on the gaussian elasticity of a network. The example of a fractal topology

By considering fractal topologies of polymer networks, we show that one can obtain much smaller values of the elastic modulus than predicted by classical models for the same density of crosslinks. In a regular fractal such as the Sierpinski gasket, one can replace the segments joining the modes by Gaussian chains. This allows one to draw some micronetworks of rank k = 1, 2 etc., with no dangling ends except for the few external points (3 for any rank). Within the frame of the phantom network model, we calculate the elastic modulus of the micronetwork. It varies as p^k−1 for p < 1, which leads, even for rather small orders k such as 2, 3, to values lower than the classical James and Guth modulus, which actually corresponds to the connectivity of a tree. Thus there is an influence of the topology. Fluctuations of the positions of crosslinks and of the distance between two crosslinks are estimated and are found to correspond to a lower deformation of the chains. Whether these topologies are more than an example and could explain the anomalies observed experimentally is a postponed discussion.     

The effect of topological constraints on polymer network pressure

Recent data on comparative osmotic deswelling of poly(acrylic acid) gels and solutions shows that the difference between osmotic pressure of the gel and of the solution, P_gel (c, f) − P_solution (c, f), taken at equal polymer concentration (c) and fraction of the ionized acrylic acid monomers (f), changes its sign from negative to positive as the concentration c increases; this effect is enhanced with increasing f whereby it is shifted toward lower concentrations. In order to explain this effect, a model is suggested for the elastic pressure of the gel network which takes into account the effect of topological constraints combined with the effect of network ionization. According to the model, the sign-change of P_gel − P_solution originates from the topological constraints on conformations of the network; the ionization of the network chains enhances this effect and shifts it to the concentration range of the experiment. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1833–1841, 1997     

Effect of annealing on the viscoelastic and viscoplastic responses of low‐density polyethylene

Two series of tensile tests with constant crosshead speeds (ranging from 5 to 200 mm/min) and tensile relaxation tests (at strains from 0.03 to 0.09) were performed on low‐density polyethylene in the subyield region of deformations at room temperature. Mechanical tests were carried out on nonannealed specimens and on samples annealed for 24 h at the temperatures T = 50, 60, 70, 80, and 100 °C. Constitutive equations were derived for the time‐dependent response of semicrystalline polymers at isothermal deformations with small strains. A polymer is treated as an equivalent heterogeneous network of chains bridged by temporary junctions (entanglements, physical crosslinks, and lamellar blocks). The network is thought of as an ensemble of mesoregions linked with each other. The viscoelastic behavior of a polymer is modeled as a thermally induced rearrangement of strands (separation of active strands from temporary junctions and merging of dangling strands with the network). The viscoplastic response reflects sliding of junctions in the network with respect to their reference positions driven by macrostrains. Stress‐strain relations involve five material constants that were found by fitting the observations. Fair agreement was demonstrated between the experimental data and the results of numerical simulation. This study focuses on the effects of strain rate and annealing temperature on the adjustable parameters in the constitutive equations. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1638–1655, 2003     

Structural rearrangement and stiffening of hydrophobically modified supramolecular hydrogels during thermal annealing

Dynamic crosslinks formed by thermoreversible associations provide an energy dissipation mechanism to toughen hydrogels. However, the details of the organization of these crosslinks impact the hydrogel properties through constraints on the network chain conformation. The physical crosslinks generated by hydrophobic association of the 2‐(N‐ethylperfluorooctane‐sulfonamido)ethyl methacrylate (FOSM) groups in a random copolymer of N,N‐dimethylacrylamide (DMA) and FOSM provide a simple system to investigate how the hydrogel structure (as determined from small angle neutron scattering impacts the mechanical properties of the hydrogel. The initial hydration of the copolymer at 25 °C leads to a kinetically trapped structure with large‐scale heterogeneities. Heating the hydrogel at 60 °C, which is above the glass transition temperature for the FOSM domains, allows the hydrogel structure to rearrange to reduce the density of network defects and the structural heterogeneities. That effectively increases the crosslink density of the network, which stiffens the hydrogel and decreases the swelling at equilibrium at 25 °C. The processing history determines how the hydrophobes aggregate to form the physically crosslinked network, whose structure defines the mechanical properties of these hydrogels. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1036–1044     

Investigating Chain Dynamics in Highly Crosslinked Polymers using Solid‐State 1H NMR Spectroscopy

Solid state ¹H NMR line‐shape analysis and (double quantum) DQ ¹H NMR experiments have been used to investigate the segmental and polymer chain dynamics as a function of temperature for a series of thermosetting epoxy resins produced using different diamine curing agents. In these thermosets, chemical crosslinks introduce topological constraints leading to residual stresses during curing. Materials containing a unique ferrocene‐based diamine (FcDA) curing agent were evaluated to address the role of the ferrocene fluxional process on the atomic‐level polymer dynamics. At temperatures above the glass transition temperature (T_g), the DQ ¹H NMR experiments provided a measure of the relative effective crosslink and entanglement densities for these materials and revealed significant polymer chain dynamic heterogeneity in the FcDA‐cured thermosets. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1143–1156     

Mechanical and thermo‐mechanical studies of double networks based on thermoplastic elastomers

A new approach to prepare and characterize double network elastomeric systems was investigated. A styrene‐ethylene‐co‐butylene‐styrene (SEBS) triblock copolymer system containing physical crosslinks was used to achieve a double network by additional crosslinking using ultra‐violet (UV) light. An ethylene–propylene–diene monomer (EPDM) terpolymer system containing chemical crosslinks was used to achieve a conventional double network using UV crosslinking. Properties from conventional monotonic tensile tests, dynamic mechanical analysis, and thermomechanical properties were investigated. These double network elastomers show a transition between competitive and collaborative behavior in their mechanical properties and lower coefficients of thermal expansion arising from a competition of the networks. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 778–789, 2010     

A new attempt to reconcile the statistical and phenomenological theories of rubber elasticity

The statistical and phenomenological theories of rubber elasticity are reviewed briefly. Combining recent concepts proposed by Yeoh and Gent, a new theory is proposed. The proposed constitutive model for rubber vulcanizates invokes two mechanisms; one influences behavior at small strains while the other dominates behavior at large strains. Network flaws, such as entanglements, are suspected to be responsible for the first mechanism. Finite extensibility of network chains is identified as the cause of the second. Thus, macroscopic behavior is directly linked to molecular concepts. The proposed theory allows prediction of the stress–strain behavior of a family of four rubber vulcanizates in different modes of deformation (simple extension, compression, and simple shear) from regression analysis of tensile data alone from just one member. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1919–1931, 1997     

Aggregation and gelation in hydroxypropylmethyl cellulose aqueous solutions

In this work we present an analysis of the thermal behavior of hydroxypropylmethyl cellulose aqueous solutions, from room temperature to higher temperatures, above gelation. We focus on significant aspects, essentially overlooked in previous work, such as the correlation between polymer hydrophobicity and rheological behavior, and the shear effect on thermal gelation. Micropolarity and aggregation of the polymer chains were monitored by both UV/vis and fluorescence spectroscopic techniques, along with polarized light microscopy. Gel formation upon heating was investigated using rheological experiments, with both large strain (rotational) tests at different shear rates and small strain (oscillatory) tests. The present observations allow us to compose a picture of the evolution of the system upon heating: firstly, polymer reptation increases due to thermal motion, which leads to a weaker network. Secondly, above 55 degrees C, the polymer chains become more hydrophobic and polymer clusters start to form. Finally, the number of physical crosslinks between polymer clusters and the respective lifetimes increase and a three-dimensional network is formed. This network is drastically affected if higher shear rates, at non-Newtonian regimes, are applied to the system.     

Fracture of model polyurethane elastomeric networks

Fracture properties of model elastomeric networks of polyurethane have been investigated with a double‐edge notch geometry. The networks were synthesized from monodisperse end‐functionalized polypropylene glycol precursors and a trifunctional isocyanate. All reagents were carefully purified and nearly defect‐free ideal networks were prepared at a stoichiometry very close to the theoretical one. Three networks were prepared: an unentangled network of short chains (M_n = 4 kg mol^?1), an entangled network of longer chains (M_n = 8 kg mol^?1) and a bimodal network with 8 kg mol^?1 and 1 kg mol^?1 chains. The presence of entanglements was found to increase significantly the toughness of the rubber, in particular at room temperature, relative to the bimodal networks and to the short chains network. Fracture experiments were carried out at different strain rates and temperatures and showed for all three networks a marked decrease in fracture toughness with increasing temperature and decreasing strain rate which mirrored reasonably well the rate and temperature dependence of tan δ, the dissipative factor. However the proportionality factor between tan δ, and G_IC was very material dependent and the shift factors obtained for the master curves of the viscoelastic properties could not be used to build fracture energy master curves. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Dynamics of polyethylene melts studied by Monte Carlo simulations on a high coordination lattice

A detailed comparison is made between the experiment, prior simulations by other groups, and our simulation based on a newly designed dynamic Monte Carlo algorithm, on the dynamics of polyethylene (PE) melts. The new algorithm, namely, noncross random two-bead move has been developed on a high coordination lattice (the 2nnd lattice) for studying the dynamics of realistic polymers. The chain length (molecular weight) in our simulation ranges from C40 (562 Da) to C324 (4538 Da). The effects of finite chain length have been confirmed and significant non-Gaussian statistics evidently results in nonstandard static and dynamic properties of short PE chains. The diffusion coefficients scale with molecular weight (M) to the −1.7 power for short chains and −2.2 for longer chains, which coincides very well with experimental results. No pure Rouse scaling in diffusion has been observed. The transitional molecular weight to the entanglement regime is around 1500 Da. The detailed mean square displacements of middle bead (g1) are presented for several chain lengths. The reptation-like slowdown can be clearly observed only above M ∼ 2400 Da. The slope 0.25 predicted by the theory for the intermediate regime is missing; instead a slope close to 0.4 appears, indicating that additional relaxation mechanism exists in this transitional region. The relaxation times extracted by fitting the autocorrelation function of end-to-end vectors with reptation model scale with M to 2.5 for long chains, which seemingly conflicts with the scaling of diffusion. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2556–2571, 2006     

Precise synthesis of well‐defined dendrimer‐like star‐branched polymers by iterative methodology based on living anionic polymerization

Dendrimer‐like star‐branched polymers recently developed as a new class of hyperbranched polymers, which resemble well‐known dendrimers in branched architecture, but comprise polymer chains between junctions, are reviewed in this highlight article. In particular, we focus on the precise synthesis of various dendrimer‐like star‐branched polymers and block copolymers by the recently developed methodology based on iterative divergent approach using living anionic polymers and 1,1‐bis(3‐tert‐butyldimethylsilyloxymethylphenyl)ethylene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6659–6687, 2006     

An experimental investigation of fracture by cavitation of model elastomeric networks

A new methodology to investigate the failure of elastomers in a confined geometry has been developed and applied to model end-linked polyurethane elastomers. The experimental in situ observations show that the elastomers fail by the growth of a single cavity nucleated in the region of maximum hydrostatic stress. Tests carried out at different temperatures for the same elastomer show that the critical stress at which this crack grows is not proportional to the Young's modulus E but depends mainly on the ratio between the mode I fracture energy G_IC and E. A reasonable fit of the data can be obtained with a model of cavity expansion by irreversible fracture calculating the energy release rate by finite elements with a strain hardening constitutive equation. Comparison between different elastomers shows that the material containing both entanglements and crosslinks is both tougher in mode I and more resistant to cavitation relative to its elastic modulus. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48:1409–1422, 2010     

Dynamic Model Metallo-Supramolecular Dual-Network Hydrogels with Independently Tunable Network Crosslinks

Hybrid polymer networks emerge between chemical and physical crosslinking, where two different modes of chain connectivity control the material behavior. However, rational relations between their microstructural characteristics, supramolecular kinetics, and the resulting network mechanics and dynamics are not well developed. To address this shortcoming, this study introduces a material platform based on a model dual-network hydrogel, comprising independently tunable chemical and physical crosslinks. The idea is realized by a click reaction between a tetra-PEG and a linear-PEG precursor, whereby the linear block also carries a terpyridine ligand at each end that can form additional physical crosslinks by metal ion–bis(terpyridine) complexation. We change the number of chemical crosslinks by varying the molar mass of the tetra-PEG, and we independently tune the metallo-supramolecular bonds by using different metal ions, Mn²⁺, Zn²⁺, Co²⁺, and Ni²⁺. Based on that modular approach, we study the rheological behavior and the diffusivity of fluorescent polymeric tracers. The dissociation of the metallo-supramolecular bonds provides a relaxation step, whose timescale and intensity are quantified by a sticky Rouse model. These two characteristics differ not only depending on the metal ion but also according to the chemical network mesh size, which highlights an interplay between the chemical and physical crosslinks. © 2020 The Authors. Journal of Polymer Science Part A: Polymer Chemistry published by Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 330–342     

Formation,structure, and elasticity of loosely crosslinked epoxy-amine networks. I. Statistics of formation

Using the theory of branching processes based on cascade substitution, relations are derived for structural parameters characterizing network formation from diepoxide, monoepoxide, and diamine for various initial compositions. The different reactivities of the hydrogen atoms of the primary and secondary amino groups (the latter being formed in the reaction) and possibly different reactivities of epoxy groups in diepoxide and monoepoxide are taken into account. Relations are derived for the critical conversion at the gel point and for changes as a function of conversion in the average molecular weight in the pregel stage, changes in the sol and gel contents, effective functionality of the crosslinks, and concentration of elastically active network chains. The derivation includes the trapping factor that appears in the theory of permanent interchain interactions (trapped entanglements) of the Langley type. An analysis of the approximation usually employed in the statistical theory based on network formation from dyads of structural units shows that this approach is quite satisfactory for small differences in the reactivities of epoxy groups in diepoxide and monoepoxide.     

Atomistic hybrid particle‐field molecular dynamics combined with slip‐springs: Restoring entangled dynamics to simulations of polymer melts

In hybrid particle‐field (hPF) simulations (J. Chem. Phys., 2009 130, 214106), the entangled dynamics of polymer melts is lost due to chain crossability. Chains cross, because the field‐treatment of the nonbonded interactions makes them effectively soft‐core. We introduce a multi‐chain slip‐spring model (J. Chem. Phys., 2013 138, 104907) into the hPF scheme to mimic the topological constraints of entanglements. The structure of the polymer chains is consistent with that of regular molecular dynamics simulations and is not affected by the introduction of slip‐springs. Although slight deviations are seen at short times, dynamical properties such as mean‐square displacements and reorientational relaxation times are in good agreement with traditional molecular dynamics simulations and theoretical predictions at long times.