Understanding the elastomeric properties of polymer networks

It is shown that Monte‐Carlo (MC) simulations of the elastic behaviour of chains in networks using realistic rotational‐isomeric‐state (RIS) chain models are able to reproduce experimentally observed deviations from Gaussian network behaviour in uniaxial extension and also to interpret, quantitatively, stress‐optical properties. In stress‐strain behaviour, an increase in the proportion of fully extended chains with increasing macroscopic strain gives rise to a steady decrease in the rate of change of the Helmholtz energy of a network, causing a reduction in network modulus at moderate macroscopic strains. There is no need to invoke a transition from affine to phantom chain behaviour as deformation increases. To evaluate stress‐optical properties, the average orientation of segments with respect to the deformation axis is calculated, taking into account the interdependence of segment orientation and chain orientation as chains become more extended and aligned under uniaxial stress. The MC method gives, in agreement with experiment, values of stress‐optical coefficient that are dependent upon both deformation ratio and network‐chain length. The method highlights serious shortcomings in the classical Gaussian model of stress‐optical behaviour. Applications of the simulation methods to the quantitative modelling of the stress‐strain behaviour of poly(dimethyl siloxane) networks and the stress‐optical behaviour of polyethylene networks are described.     

Dependence of the elastomeric properties of bimodal networks on the lengths and amounts of the short chains

Bimodal elastomeric networks were synthesized by tetrafunctionally end-linking very short and relatively long hydroxyl-terminated chains of poly(dimethylsiloxane). Decrease in the molecular weight of the short chains (from 880 to 660 to 460 g mol^?1) generally results in significant increases in ultimate strength and energy for rupture. Decrease in the number of short chains, however, causes these two quantities to go through a maximum. Too many short chains gives essentially a brittle thermoset, and this precludes any upturn in the modulus from the limited extensibility of the short chains. Having too few short chains makes their limited extensibility irrelevant since the entire macroscopic deformation can then be taken up by the long chains present in the network.     

Nonlinear elasticity of rodlike macromolecules in condensed state

The finite deformation elasticity of gels of stiff rodlike polymer chains is discussed theoretically. Unlike a rubber composed of flexible polymer chains, the elasticity of this system is energetic, and arises from the elastic deformation of the stiff chains which are forced to bend under macroscopic strain. The stress-strain curve of this system is shown to be nonlinear even if the bending of the rods is small, and has a characteristic S-shaped form which is unlike that of a rubber. The effect of orientational order is also discussed.     

Using mesoscopic models to design strong and tough biomimetic polymer networks

Using computational modeling, we investigate the mechanical properties of polymeric materials composed of coiled chains, or "globules", which encompass a folded secondary structure and are cross-linked by labile bonds to form a macroscopic network. In the presence of an applied force, the globules can unfold into linear chains and thereby dissipate energy as the network is deformed; the latter attribute can contribute to the toughness of the material. Our goal is to determine how to tailor the labile intra- and intermolecular bonds within the network to produce material exhibiting both toughness and strength. Herein, we use the lattice spring model (LSM) to simulate the globules and the cross-linked network. We also utilize our modified Hierarchical Bell model (MHBM) to simulate the rupture and reforming of N parallel bonds. By applying a tensile deformation, we demonstrate that the mechanical properties of the system are sensitive to the values of N(in) and N(out), the respective values of N for the intra- and intermolecular bonds. We find that the strength of the material is mainly controlled by the value of N(out), with the higher value of N(out) providing a stronger material. We also find that, if N(in) is smaller than N(out), the globules can unfold under the tensile load before the sample fractures and, in this manner, can increase the ductility of the sample. Our results provide effective strategies for exploiting relatively weak, labile interactions (e.g., hydrogen bonding or the thiol/disulfide exchange reaction) in both the intra- and intermolecular bonds to tailor the macroscopic performance of the materials.     

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     

Swelling,elasticity and structure of hydrogels prepared via bis-macromonomers of poly(ethylene oxide)

The effect of swelling on the shear modulus was studied for hydrogels prepared by radical polymerization of methacrylate-terminated poly(ethylene oxide) (PEO) bis-macromonomers of different molecular weight. Gels made of long chains (M = 12000 or 6000) display classical softening upon swelling, whereas gels made of shorter chains (M = 4000 or 2000) remain rigid or even stiffen. The abnormal behaviour is explained by a specific character of network junctions presented by polymethacrylate chains in which each unit is linked with a PEO network chain. It is assumed that the interactions among densely grafted PEO chains result in their stretching on polymerization and non-affine deformation on swelling, which stiffen the gel. This is verified by the data on copolymer (macromonomers - 2-hydroxyethyl methacrylate) gels that have lesser densities of PEO chains attached to the junctions and show weaker stiffening on swelling. The osmotic pressure of gels was estimated from the swelling pressure and shear modulus. Similar to the mixing pressure of equivalent PEO solutions, it varies as the 9/4 power of polymer concentration. At the same time, it is lower than the mixing pressure. This indicates that the junctions make only quantitative changes in the osmotic properties of macromonomer chains.     

Elastic behavior of simple model networks

The elastic behaviors of simple networks consisting of but a few chains have been calculated on the basis of the James and Guth theory of elasticity. The calculations show that the number of elastically effective chains in a network is less than the actual number of network chains, and that the total number of chain backbone links distribute themselves equally (approximately) among the effective chains. It is also demonstrated that a chain molecular weight distribution could be of consequence in non-Gaussian elasticity. Extrapolation of the findings to a macroscopic network suggests that the number of effective chains is one half the number of network chains, and that each effective chain behaves as if it contained twice as many of backbone links as a network chain.     

The theory of non-linear molecular orientation and stress in polymer fluids

Non-linear stress, and orientation characteristics for polymer fluids (melts, solutions) composed of chain macromolecules of finite length have been derived. Freelyjointed chains with inverse Langevin statistics have been assumed, and their behaviour in potential hydrodynamic fields analyzed. Numerical calculations have been performed for uniaxial extensional flow in a wide range of flow rates (and stresses). In the range of small stresses, orientation is a linear function of stress. At higher stresses, orientation factor levels off, asymptotically approaching unity.Flow orientation characteristics significantly differ from those derived from affine deformation of polymer networks. This difference is a natural consequence of constraints imposed by network junctions on chain deformation.This work is dedicated to Professor Hanns-Georg Kilian on his 60th birthday in appreciation of his contribution to Polymer Physics.     

Infrared spectroscopy on new multiphase thermoplastic elastomers based on hydrogen bond complexes - temperature dependence and orientation behaviour

The structure and deformation behaviour of a new class of thermoplastic elastomers is studied by temperature dependent infrared (IR) spectroscopy and by IR - dichroism spectroscopy. The thermoplastic elastomer is based on polybutadiene with statistically distributed side groups which form an anisotropic supramolecular structure via hydrogen bonds. Changes in the IR spectra at elevated temperatures are related to the melting of the ordered structure. The uniaxial deformation behaviour is studied by linear dichroism Fourier-transform (FT)-IR spectroscopy. A deformation model is developed which accounts for the major experimental results: while the polybutadiene segments behave as flexible chains with characteristic rubberlike elasticity the polar units within the supramolecular structure show an orientation behaviour characteristic for rodlike molecules.     

Model polyurethane elastomers prepared from noncrystallizable poly(propylene oxide) chains

Elastomers of controlled molecular structure were prepared from hydroxyl-terminated atactic poly(propylene oxide) (PPO) chains having number-average molecular weights M_n in the range 800–4360 g mole^?1. The chains were end-linked into noncrystallizable trifunctional networks using a specially prepared aromatic triisocyanate. The networks thus obtained were studied with regard to their stress–strain isotherms in the unswollen state, in elongation at 25°C, and with regard to their equilibrium swelling in benzene at 61°C. Values of the modulus in the limit at high deformation were in good agreement with corresponding results previously obtained on networks of poly(dimethylsiloxane) (PDMS). This is of considerable importance since use of the widely used “plateau modulus” as a measure of interchain entangling would suggest that the networks of PPO would have a much higher density of such entanglements than would the corresponding networks of PDMS. The close similarity between the moduli of the two types of networks therefore argues against the idea that such entanglements make large contributions to the equilibrium elastomeric properties of a polymer network. These values of the high deformation modulus are also in good agreement with recent molecular theories as applied to the nonaffine deformation of a “phantom” network. The values of the low deformation modulus were considerably smaller than the values predicted for an affine deformation, however, suggesting that the junction points were not firmly embedded in the network structure. This is presumably due to the relatively low degree of chain-junction entangling in the case of relatively short network chains. The swelling equilibrium results were in very good agreement with the new theory of network swelling developed by Flory.     

Molecular aspects of polymer network deformation - small angle neutron scattering and NMR studies

Poly(1,4-butadiene) networks obtained by a 4-functional random cross-linking reaction over a broad range of polymer concentration were studied by small angle neutron scattering(SANS), ²H NMR and Monte Carlo(MC) simulation in the isotropic and uniaxially deformed state. The defect structure of the networks has been characterized by MC simulation of the cross-linking reaction. The anisotropy of the radius of gyration in deformed networks determined from SANS has been analyzed by the theory of Ullman. It was found that the number of active cross-links per chain is in agreement with MC and that the chain deformation follows phantom behaviour. The local orientation as measured by ²H NMR is related to the global anisotropy of the network by a MC calculation of oriented chains. The ²H NMR line shape of the deformed network is analyzed in terms of two relaxation processes arising from interior parts of the chains and from segments at chain ends. The mobility of both decrease with strain. It was found that the orientation connected to the first process shows the classical strain dependence of rubber elasticity, whereas the second exhibits a weaker dependence on strain.     

Collapse of polyelectrolyte networks induced by their interaction with an oppositely charged surfactant. Theory

A very simple theory of swelling and collapse of weakly charged polyelectrolyte networks in the solution of an oppositely charged surfactant has been developed. The following contributions to the free energy were taken into account: free energy of volume interaction and of elastic deformation of the network chains, free energy connected with micelle formation and free energy of translational motion of all mobile ions in the system (translational entropy). Both the cases of a solution of charged surfactant and that of a mixed solution of charged and neutral surfactant components have been taken into account. It has been shown that the behaviour of the network depends on the total surfactant concentration in the system and corresponds to one of the three following regimes: At low concentration, micelles inside the network are not formed and the behaviour of the polymer network is similar to that of a network swelling in the solution of a lowmolecular-weight salt (regime 1). In the second regime, surfactant concentration inside the network exceeds the critical micelle concentration and micelles are formed; in this regime the network collapses because surfactant molecules, aggregated in micelles, cease to create “exerting” osmotic pressure in the network sample. In the third regime, at very high surfactant concentration, formation of additional micelles inside the network ceases, and the network dimensions coincide with those of the corresponding neutral network.     

Mechanochemistry unveils stress transfer during sacrificial bond fracture of tough multiple network elastomers

The molecular level transfer of stress from a stiff percolating filler to a stretchable matrix is a crucial and generic mechanism of toughening in soft materials. Yet the molecular details of how this transfer occurs have so far been experimentally unreachable. Model multiple network elastomers containing spiropyran (SP) force sensors incorporated into the stiff filler network or into the stretchable matrix network are used here to detect and investigate the mechanism of stress transfer between distinct populations of polymer strands. We find that as the filler network progressively breaks by random bond scission, there is a critical stress where cooperative bond scission occurs and the macroscopic stretch increases discontinuously by necking. Surprisingly, SP molecules reveal that even in the necked region both filler and matrix chains share the load, with roughly 90% of the SPs force-activated in the filler chains before necking still being loaded in the necked region where significant activation of the SP incorporated into the matrix chains occurs. This result, where both networks remain loaded upon necking, is qualitatively consistent with the model proposed by Brown, where holes or microcracks are formed in the stiff regions and are bridged by stretched matrix chains. Detection of merocyanine (i.e. activated SP) fluorescence by confocal microscopy shows that such microcrack formation is also active at the crack tip even for materials that do not exhibit macroscopic necking. Additionally, we demonstrate that when the ethyl acrylate monomer is replaced by hexyl methacrylate in the first network, preventing molecular connections between the two networks, the stress transmission is less efficient. This study outlines the different roles played by these multiple networks in the onset of fracture and provides molecular insights for the construction of molecular models of fracture of elastomers.

The molecular level transfer of stress from a stiff percolating filler to a stretchable matrix is a crucial and generic mechanism of toughening in soft materials.     

Study of heat treatment on the behaviour towards shrinkage,orientation and molecular order of stretched poly(vinyl chloride) fibres

The behaviour of stretched PVC fibres during thermomechanical treatments between 110–160°C has been studied. As far as shrinkage is concerned, three ranges of temperature have been characterized. Within the range 100–140°C the poly(vinyl chloride) undergoes a plastic deformation and has an elastoplastic behaviour. From 140 up to 170°C a creep phenomenon superimposes the elastic behaviour and then the polymer has a viscoplastic behaviour. As the temperature increases above 170°C there is flowing of polymer chains and the fibres break rapidly. Annealings carried out between 100 and 150°C cause the formation of ordered domains which are responsible for the formation of a temporary physical crosslinking network which hinders the shrinkage to such a temperature lower than their melting temperature. The loss of orientation of the amorphous phase is a rapid process which takes place as the temperature rises above 100°C even if the applied stress counterbalances the overall strain resulting from the potential shrinkage.     

Large deformation rheology of gelatin gels

We studied the linear and the non-linear elastic behaviour, the breaking stress and breaking strain of gelatin gels as a function of a number of experimental conditions: gelatin concentration, gelatin bloom value, ageing time, ageing temperature, pH, NaCl and CaCl₂ concentration, whey protein concentration, the amount of pre-shearing, strain rate or compression speed, using both shear deformation and compression. We analyzed the stress-strain curves using the BST-equation (Blatz et al., Trans. Soc. Rheol. 18, (1974) 145) and extracted a parameter that characterizes the linear elastic behaviour at small deformations (the moduli E or G) and one that characterizes the non-linear elastic behaviour at large deformations (the elasticity parameter n). The phenomenological BST equation describes rheological experiments adequately both in shear deformation and in compression.We found that the modulus correlates with the breaking stress. For the non-linear elastic properties of gelatin, we found that the elasticity parameter n correlates with the breaking strain Qualitatively, the non-linear elastic properties can be explained by assuming that the gelatin chains are partially in a crystalline triple helix state (the cross-links) and partially in a random coil state (the network bonds): the more extensive the rigid cross-link regions, the shorter and more stretched the network bonds become as a result of an externally applied deformation. The network bonds behave as anharmonic springs under extreme extension.Manipulation of the breaking strain was attempted in two ways: (i) by changing the (non-linear) elasticity parameter of the gel: this is possible by using a gel that has been further aged; (ii) by adding defects to the gel structure: this is possible by either pre-shearing the gel or by adding whey protein particles. The pre-shearing gives rise to a temporary effect, the addition of whey protein particles to a permanent effect.     

Segmental orientations and deformation mechanism of a poly(ether‐block‐amide) film

Simultaneous measurements of microscopic infrared dichroism, mesoscale deformation, and macroscopic stress have been made for a microphase‐separated film of poly(ether‐block‐amide) 4033 during uniaxial stretching at temperatures between 30 and 91 °C, well below the melting point of the hard polyamide‐12 (PA) domains. Before the onset of dramatic microstructural alterations, the true stress–strain relationship on the mesoscale can be described with an interpenetrating network model, and poly(tetramethylene oxide) (PTMO) soft segments undergo affine deformation. Beyond a threshold strain at which stress from the soft network becomes larger than that from the hard network, plastic deformation occurs in the hard PA domains, and this is accompanied by the downward derivations of the true stress and molecular orientation of PTMO blocks from the model predictions. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1161–1167, 2005     

Model polyurethane networks prepared from poly(ethylene oxide) and poly(tetramethylene oxide)

Polyurethane elastomers of known degrees of cross-linking were prepared from hydroxylterminated poly(ethylene oxide) (PEO) and poly(tetramethylene oxide) (PTMO) chains having numberaverage molecular weights in the range 880–6820 g mol^?1. The chains were end-linked into “model” trifunctional networks using a specially prepared aromatic triisocyanate. The networks thus obtained were studied with regard to their stress-strain isotherms in both the unswollen and swollen states, in elongation at 25°, and with regard to their equilibrium swelling in benzene at 57.9°. Values of the modulus in the limit at high deformation were in good agreement with corresponding results previously obtained on trifunctional networks of poly(dimethylsiloxane) (PDMS). Since PEO has a much higher value of the plateau modulus in the uncross-linked state, this agreement indicates that inter-chain entanglements do not contribute significantly to the equilibrium modulus of an elastomeric network. These values of the high deformation modulus are also in good agreement with recent molecular theories as applied to the non-affine deformation of a “phantom” network. The swelling equilibrium results were in very good agreement with the new theory of network swelling developed by Flory.     

三维宏观网络状囊泡薄膜的分级自组装研究

分别合成以疏水性超支化聚醚(HBPO)为核,以亲水性聚环氧乙烷(EO)和聚甲基丙烯酸N,N-二甲氨基乙酯(DMAEMA)为臂的两亲性超支化多臂共聚物HBPO-star-PEO和HBPO-star-PDMAEMA.通过两者在水溶液中的复合自组装制备得到具有pH响应性的巨型聚合物囊泡(1~10μm),并用zeta电位仪,激光共聚焦显微镜及光学显微镜对囊泡的自组装行为进行了研究.结果表明,在等电点以前,复合囊泡始终以单个囊泡形式存在;随着溶液pH的升高,囊泡逐步线型缔合成串珠结构;在更高的pH下,囊泡进一步二次聚集形成具有宏观尺度的三维蜘蛛网状超分子结构,这是一类新的自组装体.