Elasticity of real networks: Comparison of molecular theory with experiments

Predictions of the theory of elasticity of real networks are compared with results of experiments. The shape of the stress-strain curve for networks in the dry and swollen states and over wide ranges of strain, both in tension and compression, agrees with results of calculations based on the theory. The theory is also in close agreement with results of multiaxial stress-strain experiments and with the predictions of the degree of crosslinking obtained from measurements of the modulus. The theory may additionally be applied to the analysis of birefringence. The assumption of the linear additivity of the elastic and mixing free energies in a swollen network leads to results which are in agreement with experimental findings on different crosslinked systems.     

Dielectric relaxation in networks of end-linked dimethylsiloxane oligomers

Networks composed of very short dimethylsiloxane chains were prepared by end-linking dimethylsiloxane oligomers with a tetrafunctional crosslinking agent. Their dielectric properties were studied to elucidate the effects of crosslinks on molecular motion in highly crosslinked networks. The temperature of maximum loss for the primary relaxation process (α process) shifted greatly to high temperature with decrease in the chain length between crosslinks. The activation energy and the width of the absorption curve increased with decrease in chain length. No linear relation existed between the dielectric properties for the α relaxation and the crosslink density. On the other hand, the temperature of maximum loss for the secondary relaxation process (β process) shifted to high temperature with decreasing chain length, but the activation energy was almost independent of the chain length. Characteristics for the α, β and hypersonic relaxations in the networks are discussed in terms of inter- and intramolecular contributions.     

Monte Carlo simulation of two interpenetrating polymer networks: Structure, swelling, and mechanical properties

The swelling and mechanical properties of various interpenetrating polymer networks (IPNs) were studied. Six networks made from permutations of a moderately crosslinked polyelectrolyte network (ref), a moderately crosslinked neutral polymer network (net1), and a highly crosslinked polyelectrolyte network (net2) were first swollen in water and structural properties such as end-to-end chain lengths and radial distribution functions were compared with the component networks' equilibrium properties. The swelling of composite IPNs was discussed in terms of a balance between the osmotic pressure due to mobile counterions and the restoring force of the network chains, which act in parallel to counteract the osmotic swelling. For the ref-net2 system, the strong stretching of net2 chains increases the network restoring force and the further swelling due to the counterions is suppressed. The swollen networks were then uniaxially stretched, and equilibrium stress-strain plots were obtained up to high extension ratios. The equilibrium volume decreased upon uniaxial extension, and the elastic moduli of IPNs of the A-A type were slightly greater than that of their respective single networks.     

Primitive chain network study on uncrosslinked and crosslinked cis-polyisoprene polymers

In this paper, the polymer chain packing and primitive path (PP) network of uncrosslinked and crosslinked cis-polyisoprene (PI) polymer are analyzed upon employing coarse-grained molecular dynamics simulation. The crosslinking effect is found to enhance intra-chain packing of PI polymers, while weakening their inter-chain packing. Surprisingly, these effects cancel each other in the global packing behavior of this polymeric system. We systematically study the effects of molecular weight (MW) and crosslink density on the PP. Both the PP contour length and number of entanglements per chain, 〈Z〉, are found to increase linearly with MW for uncrosslinked cis-PI. The corresponding entanglement molecular length N_e of cis-PI is estimated to be 76 ± 1, in good agreement with experimental results. The polymer end-to-end distance, the PP contour length as well as 〈Z〉 of crosslinked PI are reduced by higher intra-chain packing density, compared with uncrosslinked PI, if the crosslinkers are ignored in the PP analysis. At the same time, the tube diameter of crosslinked PI is enlarged by the sparse inter-chain packing. By dividing the crosslinked cis-PI chain network into subchains through crosslinked or crosslinker beads, the PP networks of these partial systems are treated as well. We obtain scaling laws between MW/crosslinking density and 〈Z〉 for crosslinked PI polymers. The simulation results indicate that the random walk assumption, often encountered during the analysis of PPs, can only be applied to the entanglement-dominated (low crosslink density) polymers. For crosslink-dominated (high crosslink density) polymers, whose subchains have a molecular length below 100, this assumption would imply a greatly overestimated entanglement density; we thus avoid the assumption in our analysis. To our best knowledge, this is the first work to uncover the PP of crosslinked polymers.     

Structure–property relationships in photopolymerizable polymer networks: Effect of composition on the crosslinked structure and resulting thermomechanical properties of a (meth)acrylate‐based system

Photoinitiated polymer networks were formed by copolymerization of tert‐butyl acrylate with di(ethylene glycol) dimethacrylate (DEGDMA) or poly(ethylene glycol) dimethacrylate (PEGDMA). The degree of crosslinking was systematically varied by modifying the weight fraction and molecular weight of the dimethacrylate crosslinking agent. An increase in effective crosslink density with increasing crosslinking agent concentrations was confirmed by decreasing equilibrium swelling ratios (q) and increasing rubbery moduli (E_R). Glass transition temperatures (T_g) varied from ?22 to 124°C, increasing with increasing DEGDMA content and decreasing with increasing PEGDMA content. Tensile deformation behavior (at T_g) ranged from an elastomeric‐like large‐strain response for lightly crosslinked materials to a small‐strain brittle response for highly crosslinked networks. At low crosslinking levels, the strain‐to‐failure of the network polymers decreased quickly with increasing crosslinking agent concentration. The stress at failure demonstrated a more complex relationship with crosslinking agent concentration. The effect of composition on network structure and resulting properties (q, E_R, strain‐to‐failure) decreased as the crosslinking agent concentration increased. The results reveal trade‐offs in T_g, E_R, strain‐to‐failure, and failure stress with composition and network structure, and are discussed in light of the wide range of potential applications suggested in the literature for (meth)acrylate‐based photopolymerizable polymer networks including biomaterials and shape‐memory polymers. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Structure-mechanical property correlations of model siloxane elastomers with controlled network topology

We review our recent studies towards the molecular understanding of mechanical properties-structure relationships of elastomers using model polydimethylsiloxane (PDMS) networks with controlled topology. The model elastomers with controlled lengths of the network strands and known amounts of cross-links and dangling chains are obtained by end-linking the functionally terminated precursor PDMS with known molecular weights using multi-functional cross-linkers. Several modern entanglement theories of rubber elasticity are assessed in an unambiguous manner on the basis of the nonlinear stress-strain behavior of the model elastomers under general biaxial strains. The roles of cross-links and entanglements in the large-scale structure of the swollen state are revealed from small angle X-ray scattering spectra. A remarkably stretchable elastomer with the ultimate strain over 3000% is obtained by optimizing the network topology for high extensibility, i.e., by reducing the amounts of trapped entanglements and the end-to-end distance of the network strands. The model elastomers with unattached chains exhibit a pronounced viscoelastic relaxation originating from the relaxation by reptative motion of the guest chains. The relaxation spectra provide a definite basis to discuss the dynamics of guest linear chains trapped in fixed polymer networks. The temperature- and frequency-insensitive damping elastomers are made by introducing intentionally many dangling chains into the networks.     

Crosslinking of polystyrene by mono- and difunctional agents

Slightly crosslinked polystyrene networks are preferable to linear polystyrene in commercial uses where increased thermal properties are favoured. A novel method of production of macrocrosslinked networks has been developed by reaction of polystyrene with mono- and difunctional derivatives of p-xylene, durene and oligomeric chains (n<10) thereof. The reaction system consists of a common organic solvent such as acetic acid or butyl acetate and a catalyst such as H₂SO₄ or HClO₄; the reaction temperature varies between 60°C and 100°C. The degrees of crosslinking and thermal properties of the produced networks depend on the reaction system, the molar ratio of polymer to crosslinking agent and the reactivity of the functional groups; the gelation time varies between 3–12 hours for a fully crosslinked network. Promotion of the formation of regular structure networks without branches in the chains between crosslinks is achieved by the use of difunctional monomers, which favour the formation of linear polybenzylene chains between the polystyrene chains. Use of monofunctional monomers leads usually to branched and slightly crosslinked or grafted polystyrene. In both cases the regions of T_g and T_m increase up to 115°C and 350°C respectively as judged by DSC analysis. This novel crosslinking method has been also applied to crosslinking of copolymers of polystyrene and polymeric chains with aromatic structure in their backbone chain.     

Experimental tests of entanglement models of rubber elasticity: 1. Uniaxial extension-compression

The predictions of several entanglement models of rubber elasticity for the uniaxial stress-strain response of crosslinked polymer networks are examined. It is found that the Gaylord tube model and the Flory constrained junction fluctuation model both agree well with the experimental data.     

Applications of a two-network model for crosslinks and trapped entanglements

The dependence of stress and birefringence on strain in uniaxial extension of crosslinked rubbers can accurately be described by a model in which the properties of a network of crosslinks and a network of trapped entanglements are additive. The crosslink network is neo-Hookean and the entanglement network can conveniently be described by the Mooney-Rivlin equation. When the crosslinks are introduced in a state of strain near the glass transition temperature, the two networks have different reference undeformed states; they can be distinguished by appropriate measurements in the state of ease where their associated stresses are equal and opposite and in the state of deformation where the cross-links were introduced and make no contribution to the stress. When partial relaxation is permitted before crosslinking, trapping probabilities can be calculated for both relaxed and unrelaxed entanglements and compared with the Langley theory. The results are consistent with the terminal mechanism of relaxation in the tube theory of Doi and Edwards.     

Mechanical properties of interpenetrating polymer network hydrogels based on hybrid ionically and covalently crosslinked networks

Hydrogels are polymer networks swollen in water. Because of their soft and wet nature, and their ability to show large volume changes, hydrogels can be useful in many biomedical and actuator applications. In these applications, it is crucial to tune the mechanical and physical properties of a hydrogel in a controllable manner. Here, interpenetrating polymer networks (IPNs) made of a covalently crosslinked network and an ionically crosslinked network were produced to investigate the effective parameters that control the physical and mechanical properties of an IPN hydrogel. Covalently crosslinked polyacrylamide (PAAm) or poly(acrylic acid) (PAA) networks were produced in the presence of alginate (Alg) that was then ionically crosslinked to produce the IPN hydrogels. The effect of ionic crosslinking, degree of covalent crosslinking, AAm : Alg and AA : Alg ratio on the swelling ratio, tensile properties, indentation modulus, and fracture energy of IPN hydrogels was studied. A hollow cylindrical hydrogel with gradient mechanical properties along its length was developed based on the obtained results. The middle section of this hydrogel was designed as a pH triggered artificial muscle, while each end was formulated to be harder, tougher, and insensitive to pH so as to function as a tendon‐like material securing the gel muscle to its mechanical supports. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 2504–2513, 2013     

Butadiene rubbers: topological constraints and microscopic deformation by mechanical and small angle neutron scattering investigation

Summary Results of stress-strain measurements are reported for butadiene rubbers of varying crosslink density. The fluctuation of the effective tube diameter of the polymer networks was investigated under uniaxial elongation by mechanical measurements as well as by small angle neutron scattering (SANS) which probe the local orientation on a segmental scale. The effect of topological constraints on the microscopic deformation of the butadiene network chains is well described within a tube approach. For the first time, experiments at large deformations and for polydisperse sample are presented. Excellent agreement between the statistical mechanical model and the experimental results is obtained. Received: 20 November 2001 /Revised version: 5 March 2002/ Accepted: 5 March 2002     

Understanding multivinyl monomer photopolymerization kinetics through modeling and GPC investigation of degradable networks

Multivinyl monomers that react to form highly crosslinked, biodegradable networks are being developed as scaffolds for tissue engineering and vehicles for drug delivery; however, this work demonstrates their usefulness in characterizing better the complexities of the kinetics and structural evolution during crosslinking photopolymerization. The molecular weight distributions (MWDs) of the degradation products of networks formed through the free radical photopolymerization of multivinyl monomers validate a novel kinetic model to test hypotheses as to the important kinetic mechanisms during crosslinking. The kinetic model, in conjunction with the experimental results for the degradable network, provides insight into the fundamental termination mechanisms (i.e. chain length dependent termination (CLDT), chain transfer to either a unimolecular species or polymer, and the accumulation of persistent radicals) that control the MWD of the backbone kinetic chains throughout the polymerization. Specifically, the importance of CLDT during autoacceleration and the impact of light intensity on the MWD of the backbone kinetic chains are presented.     

A simple strategy to generate light-responsive azobenzene-containing epoxy networks

Azobenzene containing epoxy networks are a class of photosensitive materials characterized by high thermal, optical and mechanical stability, promising for reversible optical storage applications. Here, we propose an encouraging two-step method to fabricate crosslinked coatings by simply reacting an amine-functionalized azobenzene and an epoxy resin in bulk for specified times to get soluble products (network precursors). Thin films based on these precursors were prepared, and thermally crosslinked in order to obtain high-T_g materials. The optical response of the materials was determined, both before and after crosslinking. In the case of the samples as prepared, the dynamic time response of the system is fast, as well as the relaxation of the photoinduced birefringence, as expected due to the high mobility of the chromophore. On the other hand, crosslinked systems have a slightly slower response, but higher values of remnant birefringence, providing stability of the photoinduced orientation, what makes them promising materials to use in optical storage applications. Besides, further analysis on the effect of temperature on the induced birefringence of the polymeric networks was also conducted to help optimization of material design. Finally, we had presented some preliminary investigations of surface relief grating recording in the obtained new materials.     

Computer-Aided Design of Crosslinked Polymer Membrane Using Machine Learning and Molecular Dynamics

The formation of crosslinking network between polymer chains has significant influence on polymer properties. In particular, the crosslinked structure of ionic networks like proton exchange membrane affects the conductivity performance. To further develop in this area, a framework for polymer membrane design based on the developed quantitative prediction model of the properties of crosslinked polymer is proposed. First, polymers with different crosslinking degrees are constructed by a crosslinking algorithm. Next, molecular dynamics is used to calculate the properties of crosslinked polymers. Then, the quantitative relationship between crosslinked polymer structures and macroscopical properties is developed. Subsequently, computer-aided polymer design method is integrated with the developed quantitative predict model. The crosslinked polymer design problem is expressed as an optimization problem to obtain the optimal crosslinking degree. Bayesian optimization strategy is used to solve the established optimization model. Finally, two case studies of perfluoro sulfonic acid and perfluoro imide acid design are given to illustrate the application of the proposed polymer design framework.     

A mesoscopic network model for permanent set in crosslinked elastomers

A mesoscopic computational model for polymer networks and composites is developed as a very coarse-grained representation of the network microstructure. Unlike more complex molecular dynamics simulations, the model network is static unless undergoing deformation. The elastic modulus, which depends only on the crosslink density and parameters in the bond potential, is consistent with rubber elasticity theory, and the network response satisfies the independent network hypothesis of Tobolsky. The model, when applied to a commercial filled silicone elastomer, quantitatively reproduces the experimental permanent set and stress-strain response due to changes in the crosslinked network from irradiation.     

Structure and swelling of poly(acrylic acid) hydrogels: effect of pH, ionic strength, and dilution on the crosslinked polymer structure

The network formation of crosslinked polymer hydrogels made via a free radical polymerization mechanism is significantly influenced by the polymerization conditions. In particular, the crosslinked structure of ionic networks like poly(acrylic acid) copolymers is affected by the monomer concentration, the pH, and ionic strength during the polymerization. In this work experimental data as well as theoretical analysis are used to investigate how these factors control the degree of crosslinking and primary cyclization during the network formation of multifunctional monomers. It was found that the amount of water present during the polymerization increases primary cyclization rates, and this change affects the subsequent swelling behavior of the acrylic acid hydrogel. The effects of ionic strength and pH on the network structure are interrelated. An increase in the pH decreases the degree of primary cyclization while an increase in the ionic strength increases cyclization. To investigate further the effect of pH, a cationic polymer was formed that contained a monovinyl amine monomer and a novel diamine crosslinking agent synthesized in our laboratory. The combined effect of the ionizing backbone chain and crosslinking agent cause the degree of primary cyclization in this material to be extremely sensitive to the pH during polymerization. This result confirms the significant role of pH on the network formation in ionic materials.     

Study of three-dimensional polystyrene networks containing linear chains: 1. Influence of free chains on the volume fraction of crosslinked chains

A ternary system, crosslinked polystyrene-linear polystyrene in swelling equilibrium in benzene or cyclohexane, has been prepared by anionic polymerization in dilute solution (7.5%). By swelling ratios and modulus measurements we proposed to show the specific influence of linear polystyrene chains of high molecular weight, maintained inside the network, and to compare this behaviour with the behaviour of an ‘ideal’ polystyrene network. It may be concluded that: (i) the calculated number of elastic chains is independent of the swelling solvent, but the presence of free chains in the polymerization and crosslinking process produces a non-negligible number of free and pendant chains; (ii) for the same number of elastic chains, the two types of networks have the same swelling ratio, but the introduction of free chains into the networks leads to a decrease in the volume fraction of crosslinked chains, and thus to an increase in the swelling rate of the network. However, these values are consistent with the Gaussian theory; (iii) the values of functionality are lower than those found for ‘ideal’ networks; this result confirms the presence of pendant chains; (iv) the Flory-Huggins parameters are the same for the two types of networks.     

Polyurethane—polystyrene interpenetrating polymer networks

Two component interpenetrating polymer networks (IPN) of the SIN type (simultaneous interpenetrating networks), composed of a polystyrene network (crosslinked with divinyl benzene) and a polyester-polyurethane network (crosslinked with trimethylolpropane), were made. Electron microscopy and glass-transition measurements showed that phase separation had resulted with some interpenetration, presumably occurring at the boundaries. At a composition of about 75 percent polyurethane, a phase inversion occurred, the continuous phase being polystyrene at polyurethane compositions of less than 75 percent. The stress-strain properties and hardness measurements agreed with these results. Enhanced tensile strength was observed in the IPN's in a concentration range where modulus reinforcement was not evident. A small enhancement in tear strength and thermal stability was also noted.     

Estimation by mechanical analysis of the molecular parameters of SBR vulcanizates at different cure conditions

The changes in the network structure of SBR-1712 during vulcanization were analyzed by means of a study of the stress–strain behavior at uniaxial extension at room temperature. In order to obtain different degrees of crosslinking, samples were cured at 414 K and 433 K at several times and were characterized by a rheometer. The conformational tube model was applied for the treatment of the stress–strain measurements of vulcanized samples. This theory allows the separation of crosslink and constraint contributions to the stress–strain behavior and relevant network parameters can be estimated. In this article the change with the temperature and time of cure of the average molecular mass of the mobile network chains, the crosslink density, the microscopic lateral tube dimension, and the root-mean-square end-to-end distance of the network chain are evaluated. © 1995 John Wiley & Sons, Inc.