Bimodal networks and networks reinforced by the in situ precipitation of silica

The goal of primary interest in these investigations was the development of novel methods for preparing elastomeric networks having unusually good ultimate properties. The first technique employed involves endlinking mixtures of very short and relatively long functionally-terminated chains to give bimodal networks. Such (unfilled) elastomers show very large increases in reduced stress or modulus at high elongations because of the very limited extensibility of the short chains present in the networks. The second technique employs the in situ precipitation of reinforcing silica either after, during, or before network formation. The reaction involves hydrolysis of tetraethylorthosilicate, using a variety of catalysts and precipitation conditions, and the effectiveness of the technique is gauged by stress-strain measurements carried out to yield values of the maximum extensibility, ultimate strength, and energy of rupture of the filled networks. Information on the filler particles thus introduced is obtained from density determinations, light scattering measurements, and electron microscopy.     

Polysiloxane elastomers with bimodal chain-length distributions

Most elastomers are prepared by an adventitious, random cross-linking process and thus have a broad, unimodal distribution of network chain lengths. It is possible, however, to obtain materials of controlled chain-length distribution by restricting the reactivity of the chains to their ends, and then end linking these chains with a multi-functional reactant. The networks of this type that have proved to be of greatest interest consist of short chains end linked with long chains to yield abimodal distribution of network chain lengths. These bimodal networks have unusually high extensibility for their values of the modulus and ultimate strength, and thus considerable toughness. Most such elastometers have been prepared from chains of poly(dimethylsiloxane), by carrying out either a condensation reaction between hydroxyl-terminated chains and tetraethoxysilane, or an addition reaction between vinyl-terminated chains and a poly(methylhydrogen siloxane) oligomer. The present review discusses the preparation of such materials, the characterization of some of their properties, and the interpretation of these properties in terms of the molecular theories of rubberlike elasticity.Presented at the XXVIth Silicon Symposium, Indiana University-Purdue University at Indianapolis, March 26–27, 1993.     

Improvements in the stress-strain behavior of urethane rubbers by bimodal network formation

Urethane rubbers find increasing application as binders for composites. Typical examples are solid propellants. The rubber networks are formed by end linking hydroxy-terminated prepolymers with tri- or higher functional isocyanates. A recent trend in solid propellant technology is the replacement of the traditional low-energy binders with “energetic” binders containing nitro, nitrato, or azido groups. Since these energetic polymers create relatively short interchain lengths between the cross-link points, the binders give notoriously poor mechanical properties. Our study demonstrates that significant improvements in the stress-strain behavior are attained with bimodal modifications of the energetic binders, that is, by blending these energetic short chains with very long chains prior to curing into rubbers. Molecular aspects of the improvement have been examined in terms of polymer types, crosslinkers, viscoelastic factors, and solid filler content. Results indicate that the improvement is primarily due to the extent of nonaffine deformation of the bimodal rubber network.     

Some novel polysiloxane elastomers and inorganic-organic composites

This review describes the use of polysiloxanes in developing two novel types of materials. In the first approach, polysiloxane elastomers were prepared so as to have unusual network chain length distributions, thereby improving their ultimate properties. The technique involved end linking mixtures of very short and relatively long functionally terminated chains of poly(dimethylsiloxane) to give bimodal networks. Such (unfilled) elastomers show very large increases in reduced stress or modulus at high elongations because of the very limited extensibility of the short chains present in the networks. This non-Gaussian behavior also appears in compression or biaxial extension, as obtained by inflation of sheets of the material. Non-Gaussian theories taking into account this limited chain extensibility were found to be in good agreement with experiment. The composites were prepared using techniques very similar to those employed in the sol-gel pproach to ceramics. Alkoxysilanes or related metaloorganic materials were hydrolyzed in the presence of polymer chains, for example, polysiloxanes and polyoxides, that have reactive end groups such as hydroxyls. The end groups bond the polymer chains into the silica or related ceramic material formed in the hydrolysis, thus forming inorganic-organic composites. When the polymer chains are in excess, they constitute the continuous phase, with ceramic-type material appearing as reinforcing domains. When present in smaller amounts, the polymer is dispersed in the continuous ceramic phase, to give a polymer-modified ceramic. Under some conditions, bicontinuous systems are obtained. The composites thus prepared were characterized by stress-strain measurements, density determinations, differential scanning calorimetry, electron microscopy, X-ray and neutron scattering, and NMR spectroscopy.This review was presented at the Second International Topical Workshop, Advances in Silicon-Based Polymer Science.     

The use of model polyisobutylene networks to study strain-induced crystallization

Summary Model elastomeric networks were prepared by trifunctionally end linking hydroxyl-terminated chains of polyisobutylene having number-average molecular weights in the range 10^–3M_n = 2.4 – 10.7 g mol^–1. Their stress-strain isotherms in elongation at 25°C in the unswollen state showed significant increases or upturns in modulus at high elongations, due to strain-induced crystallization. Increase in degree of cross-linking (decrease in M_n) was found to decrease the elongation required to initiate crystallization and the maximum extensibility, but to increase the magnitude of the upturn in modulus.     

Stress-strain isotherms for polymer networks at very high elongations

Some polymer networks show an anomalous increase in the modulus or reduced stress at very high elongations. This behavior has now been investigated definitively by determining stress-strain isotherms for both crystallizable and noncrystallizable networks, prepared using several curing techniques (carried out so as to yield a wide range in degree of cross-linking). The networks were studied unfilled at a number of temperatures, and at several degrees of swelling. The results clearly implicate strain-induced crystallization as the origin of the upturn in the modulus, and thus demonstrate that the wide spread interpretation of this upturn in terms of limited chain extensibility is incorrect.     

Molecular modelling of the elastic behaviour of poly(ethylene terephthalate) network chains

The Monte-Carlo (MC) method developed to model the elastomeric stress-strain behaviour of polyethylene (PE) and poly(dimethyl siloxane) (PDMS) networks and the stress-optical behaviour of PE networks is now applied to the stress-strain behaviour of poly(ethylene terephthalate) (PET) networks. In keeping with the previous results for PE and PDMS networks, increases in the proportions of fully extended chains with macroscopic deformation are found to give rise to steady decreases in the rates of Helmholtz energy changes, causing reductions in moduli at moderate macroscopic deformations. There is no need to invoke a transition from affine to phantom chain behaviour as deformation increases.By using rotational-isomeric-state (RIS) models of the network chains and the MC method, stress-strain behaviour can be related to chemical structure. In this respect, the greater conformational flexibility of the PET chain leads to lower network moduli and smaller deviations from Gaussian network behaviour than for PE networks. In addition, the stiff, aromatic section of the PET repeat unit structure is seen to endow particular characteristics on the end-to-end distribution functions of PET chains. These characteristics are taken fully into account in evaluating the elastomeric properties of the PET networks. Subsequent publications will apply the present results to interpreting the measured stress-strain and the stress-optical properties of entangled PET melts.     

Elastomers with two crosslinking systems of different lengths viewed as bimodal networks

Elastomers cured with two crosslinking systems such as sulfur and the polymerization products of p-benzoquinone are shown to have much improved overall mechanical properties. It was thought that this was because of the antioxidizing potency of the quinone polymers that act as radical traps during the oxidative degradation process. However, if the polyquinone crosslinks of the greater length themselves act as elastomeric network chains, then a bimodal network with its, exceptional mechanical properties is produced. Adding commercial antioxidants to the samples will even harvest much tougher samples. The antioxidant added, along with the quinone polymers, will reserve the integrity of the bimodal network produced and lead to better mechanical properties. Tests were also done to examine the effect of the quinone polymers on the hardness and on the onset of the vulcanization process. © 1996 John Wiley & Sons, Inc.     

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.     

Toughness and fracture energy of PDMS bimodal and trimodal networks with widely separated precursor molar masses

End-linked PDMS bimodal and trimodal networks display enhanced mechanical properties in uniaxial extension over those of unimodal networks with similar modulus when the molar masses of their precursor chains are widely separated. These multimodal networks have optimal mechanical properties when the short chains are near their overlap concentration and sustain most of the load, but the volume of the system is still dominated by the ductile long chain component. Such elastomers can be stretched to large elongations before fracture while displaying an upturn in stress at high strain. Improvement in fracture energy of pre-cut bimodal and trimodal networks over that of unimodal networks is much less pronounced and appears to be dictated by the average molar mass of the effective elastic strands in each network.     

The effects of temperature and molecular weight on the mechanical response and strength of elastomers

Summary Constitutive equations are derived for the mechanical behavior of rubbery polymers at finite strains. The model is based on the concept of rigid-rod networks, where breakage of chains is treated as bond scission. Adjustable parameters in the stress-strain relations are found by fitting observations in tensile tests for ethylene-octene copolymers. It is revealed that the constitutive equations correctly describe stress-strain curves up to the break points. Young's modulus and the critical strength per bond monotonically decrease with temperature and increase with molecular weight. Received: 17 January 2001/Accepted: 27 February 2001     

Modeling the elastomeric properties of stereoregular polypropylenes in nanocomposites with spherical fillers

The elastomeric properties of networks of stereoregular polypropylenes (PP) filled with spherical nanoparticles have been modeled in an attempt to obtain better insights into elastomer reinforcement. The polymers were either isotactic or syndiotactic PP in the amorphous state, and the simulations were based on rotational isomeric state (RIS) theory combined with the largest eigenvalue method for deriving conditional bond probabilities. Monte Carlo simulations gave distributions of the end-to-end distance of these chains in the presence of the particles, and these were used in the Mark-Curro theoretical approach to calculate values of the normalized stress, and the reduced stress (shear modulus) under uniaxial stretching. The simulations were calculated for PP chains having 100-200 skeletal bonds, for several temperatures from 481 to 650 K, and for varying filler particle sizes (up to 100 Å). The presence of the filler nanoparticles was found to influence chain conformations, frequently leading to significant chain extensions, which significantly affect the elastomeric properties of the nanocomposites.     

The Effects of Network Imperfections on the Small-Strain Moduli of Polydimethylsiloxane Elastomers Having High Functionality Cross Links

Abstract

Poly(dimethylsiloxane) networks of high cross-link functionality have been prepared by end linking vinyl-terminated chains with multifunctional poly(methylhydrosiloxane) chains. They covered a wide range in the extent of reaction, P_vi , of the vinyl end groups. At small strains, these networks had elongation moduli that significantly exceeded the values predicted by the Flory-Erman theory. Neglected in such standard analyses, however, is the fact that the segments between cross links along the junction precursor molecule can themselves act as short network chains, contributing to the modulus and giving a strongly bimodal distribution of both network chain lengths and cross-link functionalities. As would be expected, an unmistakable transition is observed in values of the shear modulus G toward the phantom limit of deformation as the crosslink density increases. Calculations based on recognition of such short chains give results in much better agreement with experiment. The results so obtained showed strong dependence of the elastomeric properties on the extents of reaction and the inherent network imperfections. Such imperfections have a pronounced effect on the equilibrium modulus, more specifically on the empirical constant 2C ₂. The dependence of 2C ₂ on the volume fraction of the elastically “effective” chains is thus established. Moreover, the results unambiguously demonstrate that the empirical constant 2C ₂ is essentially a topological contribution and contains no contributions from the chemical network.     

Some dynamic mechanical properties of unimodal and bimodal networks of poly(dimethylsiloxane)

Summary Elastomeric networks of polydimethylsiloxane prepared by end-linking chains having molecular weights in the range 18,500 to 220 g mol^-1 were studied from -128 to 50°C using a Rheovibron DDV III Viscoelastometer. In the case of the unimodal networks, the glass transition temperature T_g was generally insensitive to degree of cross-linking. The intensity of the tan δ relaxation, however, increased by over an order of magnitude over the range of cross-link densities investigated. Bimodal networks prepared from mixtures of relatively long and very short PDMS chains also had values of T_g which were insensitive to degree of cross-linking. Finally, as expected, the intensities of the tan δ peak for the bimodal networks could not be explained on the basis of simple additivity of contributions from the relatively long and the very short network chains.     

Molecular dynamics simulations of deformation mechanisms of amorphous polyethylene

Molecular dynamics simulations were used to study deformation mechanisms during uniaxial tensile deformation of an amorphous polyethylene polymer. The stress-strain behavior comprised elastic, yield, strain softening and strain hardening regions that were qualitatively in agreement with previous simulations and experimental results. The chain lengths, number of chains, strain rate and temperature dependence of the stress-strain behavior was investigated. The energy contributions from the united atom potential were calculated as a function of strain to help elucidate the inherent deformation mechanisms within the elastic, yield, and strain hardening regions. The results of examining the partitioning of energy show that the elastic and yield regions were mainly dominated by interchain non-bonded interactions whereas strain hardening regions were mainly dominated by intra-chain dihedral motion of polyethylene. Additional results show how internal mechanisms associated with bond length, bond angle, dihedral distributions, change of free volume and chain entanglements evolve with increasing deformation.     

Experimental characterisation and further molecular modelling of the conformational and elastic behaviour of poly(ethylene terephthalate) network chains

The Monte-Carlo (MC) method developed to model the elastomeric stress-strain behaviour of polyethylene (PE), poly(dimethyl siloxane) (PDMS) and poly(ethylene terephthalate) (PET) networks and the stress-optical behaviour of PE networks is now developed to investigate further the stress-strain behaviour of PET networks. Accurate infrared (IR) spectrometry measurements have been used to determine the populations of gauche conformers in the glycol residues of PET chains in melts. The proportion of gauche states was found to be 76%, consistent with the rotational energy difference of −4.16 kJ mol⁻¹ between trans and gauche states used previously.The greater conformational flexibility of the PET chain compared with the PE chain leads to lower network moduli and smaller deviations from Gaussian and affine network behaviour. Previous results are briefly reviewed and new comparisons of the elastic behaviour of PET and PE chains are made using normalised plots. Subsequent publications will apply the present results to interpreting the measured stress-strain and the stress-optical properties of entangled PET melts.     

拉伸过程中橡胶交联网络结构变化研究

研究拉伸过程中乳聚丁苯橡胶交联网络结构的变化情况.试验结果表明:硫黄用量对交联密度和交联键类型均有影响;微小变形下,利用交联密度通过统计力学理论计算得出的硫化胶模量理论值增量与实测值增量具有较好的一致性;在拉伸过程中,硫化胶总交联密度减小;与转变点(应力-应变曲线拐点)相比,断裂点硫化胶的总交联密度变化不大,但单双硫键交联密度增大,且增量与拉伸初期硫化胶多硫键含量线性相关,说明断裂的部分多硫键重组为单双硫键.     

Matrix models of discretely bending, stiff polymers

Polymer models which make use of the Ising model and transfer matrix techniques remind us, for example, of the work of Flory [Statistical mechanics of chain molecules, 1969] and Zimm and Bragg [J Chem Phys, 31 (1959) 526]. We investigate the properties of some such polymer models where the chain conformation can be described solely by an Ising-like parameterization and a set of independent, predetermined bond direction vectors or by a Potts-like model for directions of bond vectors on a lattice, with the specific aim of understanding more closely the connection of constraints and forces on the chain ends for polymers which, in general, are of arc length corresponding to their persistence lengths. Instances of these models are directed helical walks, random sequential walks, bimodally distributed in direction walks or relatively short, stiff chains fixed into a network. The behavior of this model under deformation in statistical mechanics and its dynamical properties under Glauber dynamics are discussed.     

Effect of chain length distribution on thermal characteristics of model polytetrahydrofuran (PTHF) networks

A series of model polytetrahydrofuran (PTHF) networks were synthesized via end-linking reactions of α, ω-allyl PTHF oligomers with a stoichiometric tetrafunctional crosslinker. The telechelic PTHF oligomers were synthesized by living cationic ring-opening polymerization of tetrahydrofuran followed by a termination reaction with allyl alcohol. Networks thus prepared have well-controlled architecture in terms of the inter-crosslink chain length (M_c) and chain length distribution: resulting in unimodal, bimodal and clustered structures. Unimodal network was prepared by using polymer chains of same molecular weight, bimodal networks were synthesized by using two groups of polymer chains with different average molecular weights, and the clusters are prepared by incorporating clusters of networks with small molecular weight chains in a network matrix made of longer chains. Thermal characteristics of these model networks were investigated as a function of crosslink density, as well as inhomogeneities of crosslink distribution using DSC. We demonstrate that glass transition temperature (T_g) and crystallization behavior (melting temperature and crystallinity) of the networks are both strongly influenced by crosslink density (M_c). By comparing the unimodal, bimodal and clustered networks with similar average M_c, the effects of inhomogeneities in the crosslink distribution on the thermal properties were also investigated. Results show that inhomogeneities have trivial influence on T_g, but strongly affects the crystallization behavior. Moreover, the effects of the content ratio and length ratio between long and short chains, and the effects of cluster size and size distribution on the thermal characteristics were also studied.     

Physical properties of some organophosphazene copolymers. II. Thermoelasticity andin situ reinforcement of the cross-linked networks

Aryloxy phosphazene copolymers with phenoxy andp-ethyl phenoxy substituents were cross-linked into elastomeric networks and studied with regard to their stress-strain and thermoelastic (force-temperature) behavior. The thermoelastic results showed that the energetic contribution to the elastic force was negative, indicating that the unperturbed dimensions of the polymer chains decrease with increases in temperature.In situ precipitation of silica into the elastomers by hydrolysis of an absorbed alkoxysilane was found to give excellent network reinforcement.