Characterization of nonideal networks by stress-strain measurements at large extensions

It is shown how a characterization of unfilled, amorphous rubber networks can be evaluated from uniaxial stress-strain measurement data. Beside the cross-linking density, the relative scission probability during the curing procedure is evaluated, which determines the amount of dangling free chain ends and the number of trapped entanglements. These values are found from the C₂ term of the Mooney-Rivlin equation by using the predictions of a tube model. A necessary requirement for applying stress-strain measurements at large extensions is the consideration of the finite extensibility component of the reduced stress. It is taken into account by using a numerical procedure, which derives from a series expansion of the inverse Langevin approximation. The experimental results found at natural rubber networks cross-linked with thiuram (TMTD) and peroxid (DCP) show that network defects cannot be neglected in the DCP networks. They are assumed to be connected to the worse tensil strength properties compared to the TMTD networks. © 1993 John Wiley & Sons, Inc.     

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.     

Comparison of recent rubber-elasticity theories with biaxial stress-strain data: the slip-link theory of Edwards and Vilgis

The Edwards-Vilgis (EV) slip-link theory (1986) derives the elastic free energy of a rubber-like network model containing stable and sliding network junctions (crosslinks and slip-links) and predicts both low-strain softening and high-strain hardening. The four-parameter stress-strain relations calculated by the theory for geometrically different deformation modes up to high strains were tested experimentally using published biaxial stress-strain data on simple covalently crosslinked networks. For networks with low degrees of strain softening and low extensibilities, the experimental dependencies could be described rather well but, generally, a simultaneous satisfactory fit to uniaxial, pure shear and equibiaxial data was not obtained. Systematic experiment-theory deviations exceeding 10% were observed and some of the parameters had a tendency to assume values lying outside the reasonably expected range. The prediction of a pronounced maximum in the strain dependence of stress supported by slip-links seems to be a reason for the discrepancy. Also, modeling of the high-strain singularity in entropy is done in the EV theory using a rather simple approximation. As a result, the finite extensibility contribution to the stress of a slip-link-free network model becomes improbably high and significantly exceeds that following, at a given modulus and locking stretch, from the rigorously derived Langevin-statistics-based eight-chain-network elasticity theory of Arruda and Boyce.     

The effect of strain-induced crystallization on the ultimate properties of an elastomeric polymer network

Elastomeric networks made up of chain molecules of sufficient structural regularity generally exhibit strain-induced crystallization. Crystallites thus formed have a pronounced reinforcing effect within the network, and thus increase its ultimate properties (ultimate strength and maximum extensibility), Increase in temperature or addition of diluent (plasticizer) suppresses the strain-induced crystallization and thus diminishes the ultimate properties. These effects are demonstrated using stress-strain isotherms obtained in elongation for crystallizable networks of cis-1, 4-polybutadiene and of polyisobutylene. The magnitude of the effects of strain-induced crystallization are determintud by comparisons of the ultimate properties of these two crystallizable networks with the corresponding ultimate properties of noncrysrallizable networks of polydimethylsiloxane.     

Experimental and theoretical investigations on petroleum-based elastomers with two cross-linking systems of different lengths viewed as bimodal networks

A review with 36 references discussing the chemistry and the structure-property relationship of elastomers cured with two cross-linking systems of different chain lengths such as sulfur and the polymerization products of p-benzoquinone and viewed as bimodal networks. These exceptional networks have shown remarkable improvements in the overall mechanical properties which are anticipated to be due to the non-Gaussian effects known for bimodal networks and evident by the anomalous upturn in the modulus values in Mooney-Rivlin stress-strain data representations. Proton and ¹³C NMR as well as energy minimization calculations were used to study the chemical structures and single chain contributions of polyquinones. Nuclei bending of these oligomers have shown to be greatly influenced by the restricted torsional behavior due to the presence of the hydrogen bonds between the benzenoid nuclei. Intrinsic atomic-level forces for the networks were evaluated using molecular dynamics techniques and showed that while the forces acting on the junction points of the cross-linking segments and the elastomeric chains had no apparent change as a consequence of the networks' bimodal formation, forces acting on the short chains of the bimodal networks are of much higher values as compared to those of unimodal networks. The presence of the relatively long polyquinone chains in the bimodal networks has caused the short sulfur chains to stretch to its maximum extensibility and no longer can increase its end-to-end distance separation by simple rotations about its skeletal bonds. Limited chain extensibility of the short chains resulting from the deformation of the bond angles and bond lengths has lead to higher potential energies. Studies on the swollen bimodal networks have validated the above conclusions since swelling of the networks will prevent the elastomeric chains from undergoing possible strain-induced crystallization during the stress-strain experiments and any abnormalities in the mechanical behavior of these networks must be therefore the result of the limited extensibility of the short chains of the networks.     

Synthesis and characterization of free radical cured Bis-methacryloxy bisphenol-A epoxy networks

Synthesis and free-radical curing reaction of the bisglycidylmethacrylate of bisphenol-A (Bis-GMA) were investigated. Bis-GMA resin was synthesized by reacting Epon 825 with methacrylie acid, followed by characterization using IR and NMR spectroscopy. Various modifiers having reactive double bonds were co-cured with the methacryloxy resins using a free-radical initiator. The networks obtained were compared with a cycloaliphatic amine-cured epoxy network. Thermal characterization shows that methacryloxy-cured systems are more resistant to mechanical penetration and have higher glass-transition temperatures and better stability with regard to thermal decomposition as compared with the conventional diamine-cured epoxy networks. Dynamic mechanical experiments and stress-strain tests also indicate that Bis-GMA based networks have higher tensile moduli and lower elongation at break. Using different modifiers such as 2-ethylhexyl acrylate, the tensile and impact properties of the networks can be improved.     

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.     

Elasticity of urethane networks

Various polymer networks have been prepared based on poly(propylene oxide) which has been linked either by urethane groups or ester groups. These networks have been examined by stress-strain measurements to find the degree of deviation from ideal rubber elasticity (as specified by the statistical theory) and by neutron scattering to find the mobility of the poly(propylene oxide) chain. The stress-strain results showed the urethane-linked networks to be identical to the ester-linked networks as long as there were no short chain polyols in the formulation. Networks containing short chain polyols have a greater deviation from ideal rubber elasticity. The neutron scattering results showed the ester-linked poly(propylene oxide) to have the same mobility as an uncrosslinked poly(propylene oxide), whereas urethane-linked networks have a lower mobility, similar to an analogous urethane-linked polymer. A small effect of crosslinking was observed. The results are explained in terms of some phase separation occurring in the polyurethanes only when short chain polyols are present. In the simple urethane-linked networks the poly(propylene oxide) chain mobility is reduced by hydrogen bonding to the urethane groups, but this has no effect on the equilibrium stress-strain properties.     

Polysiloxane-Cellulose acetate butyrate cellulose interpenetrating polymers networks close to true IPNs on a large composition range. Part II

Interpenetrating polymer networks combining cellulose acetate butyrate (CAB) and α,ω-divinyl-polydimethylsiloxane (PDMS) in different weight proportions have been synthesized. The synthesis involves a one pot-one shot process in which all components are first mixed together. For each composition, the relative CAB and PDMS network formation rates are adjusted through the concentration of DBTDL used as CAB network formation catalyst. Thus, the chemically independent networks are formed quasi-simultaneously in order to avoid phase separation. The CAB cross-linking density effect on the PDMS/CAB IPN mechanical properties has also been particularly studied. All synthesized IPNs are transparent and only one mechanical relaxation temperature lying between those of the single CAB and PDMS networks is observed by DMTA analysis. These results show that the networks are correctly interpenetrated and no phase separation is observed at the DMTA level. Some mechanical properties of the PDMS network are significantly improved in this IPN combination and their stress-strain behavior has highlighted a synergistic effect arising from the IPN architecture. Thus, these IPNs exhibit many characteristics, which would allow defining them as close to ‘true’ IPNs.     

Studies on double networks in natural rubber vulcanizates

The concept of double networks is a rather new idea, by which one imparts chain orientation in elastomers. Double networks were made in natural rubber vulcanizates cured with a single and a new binary accelerator system. Double networks with different extensions were prepared and their effects on tensile properties were analyzed. The influence of extent of initial cure on double‐network formation was examined. Thermal stability of the double network formed was analyzed by ageing of the double networks and was found to improve with residual extension. Crosslink density of the networks formed was determined by swelling methods and stress–strain analysis. It was found that crosslink density increased with double‐network formation and residual extension. The stress–strain behavior and moduli were analyzed to study the effect of these properties on double‐network formation. Double networks were hardly affected by the binary accelerator system. Based on the studies it was found that residual extension was the major factor determining the final properties. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 1068–1076, 2004     

The phenomenon of double yielding in polyamide 6/K resin blends

Summary The polyamide 6 (PA6)/K resin (K) blends of some kinds of compositions have been prepared by extrusion. During the process of tensile testing, we found that the PA6/K blend with 10% PA6 has the usual stress-strain behavior, and that the samples obtained with 30% and 50% PA6 show apparently double yielding behavior, while the PA6/PS blend does not show the double yielding phenomenon at all same mass ratio. Considering the microscopic morphology study and results of mechanical properties of the PA6/K blends, the first yield point which occurs at the lower tensile stress might be caused by the deformation of the K resin matrix, and the second one may be correlated to the permanent plastic deformation of the entanglement of PA6 chains and PB segments within chains of K resin.     

高分子材料极限断裂强度和破坏性能的研究(Ⅰ)等速拉伸下聚合物网极限断裂强度的动力学理论

本文提出了一种等速拉伸下聚合物网极限断裂强度的动力学理论.从化学活化反应速度理论和橡皮大形变弹性分子理论出发,建立了以链的应力集中系数为变量的断链动力学方程.得到了等速拉伸下聚合物网的极限断裂状态方程,成功地把极限断裂性能同聚合物网的结构和测试条件联系起来.并用4种聚合物网的极限断裂性能数据验证了该理论,得到了理论同实验很好地符合,亦为建立聚合物的破裂包络线提供了理论基础.     

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.     

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.     

Material and finite element analysis of poly(tetrafluoroethylene) rotary seals

Abstract

The stress-strain characteristics of PTFE under uniaxial tension and compression have been measured at various temperatures. A new finite element analysis procedure using MARC is presented, which can simulate the different properties of PTFE from tension and compression data. This method is based on using the maximum principal stress value at the integration point of each element to define whether the element is under tension or compression at each increment, then using subroutines to specify the material properties. A positive value indicates a state of tension and a negative value indicates compression. It has been found that the finite element analysis results are in good agreement with those from experiment. Finally, a PTFE rotary seal was modelled using this new method, and results were obtained incorporating stress and lip loads of the rotary seal, with different temperature effects.     

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.     

Fourier transform infrared and high-resolution solid-state carbon-13 NMR spectroscopic characterization of cured polystyrylpyridine resins

Interesting crosslinked materials possessing good mechanical and thermal properties are obtained by condensation of 2,4,6-trimethylpyridine (collidine) with terephthalic aldehyde in the presence of an acidic catalyst. Fourier transform infrared spectroscopy has been used to follow the kinetics of the chemical reactions involved in the formation of the tridimensional network using aldehyde and ethylene absorption bands. The first steps of the reaction consist in the addition of aldehyde groups on the methyl groups of collidine followed by a dehydration reaction which leads to the formation of ethylenic functions. Crosslinking is obtained by an addition reaction of the methyl groups of collidine on the double bonds created in the first processes. These reactions are strongly dependent on the reaction temperature. Cured resins prepared with different acidic catalysts have been studied by carbon-13 NMR. p-Toluene sulfonic acid leads to residual aldehyde groups in the cured resins whereas no residual aldehyde groups are observed after a relatively short curing time when sulfuric acid is used as the catalyst. The networks created in the two cases are not equivalent and present different mechanical properties.