Effect of crosslink density on the creep behavior of natural rubber vulcanizates

Torsional creep measurements on four natural rubber vulcanizates, crosslinked to different degrees, were carried out in the temperature range from ?50 to 90°C. This investigation complements the studies on identical samples of the stress relaxation behavior by Chasset and Thirion and of the dynamic mechanical response by Ferry, Mancke, Maekawa, ōyanagi, and Dickie. The creep measurements reported are shown to be in agreement with the stress relaxation results. In addition to the usual temperature reduction, a superposed curve was obtained for the long time response using the apparent molecular weight between crosslinks, M_c, as a reduction variable. The variation in viscoelastic response with crosslink density is interpreted as a restrictive action of the chemical crosslinks on the transient entanglement network.     

Isothermal and nonisothermal creep of lightly crosslinked cis-1,4 polybutadiene

A nonisothermal creep experiment has been analyzed to ascertain its suitability for determining the temperature dependence of low activation energy viscoelastic processes in elastomers far above T_g. The nonisothermal method was employed to determine the activation energy for creep near 35°C in a lightly crosslinked cis-1,4 polybutadiene elastomer at small strains within the linear viscoelastic region, and at various large deformations up to rupture. The observed activation energy was essentially independent of the level of strain, and the value of ΔH_a (～11 kcal/mole) determined via the nonisothermal creep method was in good agreement with the result (～12 kcal/mole) obtained via time-temperature superposition of isothermal linear viscoelastic creep data. The nonisothermal data allowed for an estimate of the volume of the “flow unit” associated with the controlling viscoelastic creep mechanism, attributed here to slippage of entanglements within the lightly crosslinked network.     

Linear thermoviscoelasticity and characterization of noncrystalline EPDM rubber networks

An experimental study has been made to specify how the time-temperature superposition and the linear viscoelastic characteristics vary with the degree of crosslinking for a broad class of noncrystalline peroxide-cured EPDM networks. A new, very sensitive method is applied to determine the horizontal and vertical shift functions in an independent way. All uncrosslinked samples are thermoelasticoviscously simple with horizontal shift functions a_T of the WLF type and vertical shift functions almost independent of temperature, in agreement with recent theoretical understanding. Upon crosslinking, these materials become thermoviscoelastically complex networks, but superposition can still be accomplished by assuming different temperature dependences for the relaxational strength and the equilibrium modulus. The a_T functions can be taken independent of the degree of crosslinking. The vertical shift functions b_T for the relaxational strength vary with the degree of crosslinking between theoretical predictions for uncrosslinked and perfectly crosslinked EPDM networks. The equilibrium moduli of the lightly cured networks decreases with increasing temperature, which is ascribed to the presence of interchain associations between ethylene sequences in the trans state. Upon further crosslinking, these effects gradually vanish and eventually the networks can be described as viscoelastically simple with an energy elastic contribution due to the ethylene trans-gauche transitions. The linear viscoelastic characteristics, namely the storage and loss moduli and compliances and phase-angle master curves and the relaxation and retardation spectra are discussed as a function of the degree of crosslinking. A sol/gel analysis and equilibrium swelling measurements complete the experimental characterization of three familes of five EPDM networks each.     

Creep behavior of amorphous ethylene–styrene interpolymers in the glass transition region

The viscoelastic behavior of amorphous ethylene–styrene interpolymers (ESIs) was studied in the glass transition region. The creep behavior at temperatures from 15°C below the glass transition temperature (T_g) to T_g was determined for three amorphous ESIs. These three copolymers with 62, 69, and 72 wt % styrene had glass transition temperatures of 11, 23, and 33°C, respectively, as determined by DMTA at 1 Hz. Time–temperature superposition master curves were constructed from creep curves for each polymer. The temperature dependence of the shift factors was well described by the WLF equation. Using the T_g determined by DMTA at 1 Hz as a reference temperature, C₁ and C₂ constants for the Williams, Landel, and Ferry (WLF) equation were calculated as approximately 7 and 40 K, respectively. The master curves were used to obtain the retardation time spectrum and the plateau compliance. The entanglement molecular weight obtained from the plateau compliance increased with increasing styrene content as 1,600, 1,870, and 2,040, respectively. The entanglement molecular weight of the ESIs was much closer to that of polyethylene (1,390) than to that of polystyrene (18,700); this was attributed to the unique chain microstructure of these ESIs with no styrene–styrene dyads. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2373–2382, 1999     

Rubber networks containing unattached macromolecules. I. Linear viscoelastic properties of the system butyl rubber–polyisobutylene

Mixtures of butyl rubber with polyisobutylene (molecular weights 0.055 and 2.3 × 10⁶) up to 50% by weight were crosslinked by sulfur, leaving the polyisobutylene molecules free to reptate in the butyl rubber network. Linear viscoelastic properties were measured in shear creep for periods up to 5 × 10⁵ sec at 25°C and oscillating shear deformations from 0.1 to 3 Hz, at temperatures from 2 to 63°C. Comparison with the properties of a butyl rubber crosslinked without polyisobutylene showed contributions to creep and mechanical loss attributable to the reptating species. Comparison with the properties of polyisobutylene (higher molecular weight) showed that the relaxation times associated with the reptating species in the upper part of the terminal zone are the same for different polyisobutylene contents (25% and 50%) and for 100% polyisobutylene in which no permanent network is present; their contributions to modulus appear to be proportional to the volume fraction of polyisobutylene to a power of about 2/3. The time required in stress relaxation for the portion of the modulus attributable to the reptating species to decay to half its plateau value is, based on the two molecular weights employed, proportional to the polyisobutylene molecular weight to the third power. The magnitude of the associated mechanical loss and its location on the frequency scale can thus be controlled independently.     

Thermomechanical behavior of a polyphenylquinoxaline

Crosslinking of linear poly[2,2′-(1,4-phenylene)-6,6′-bis(3-phenylquinoxaline)] (PPQ) by isothermal heat exposure in the temperature range between 425 and 490°C was investigated by means of torsional braid analysis. The change in glass transition temperature due to isothermal exposure was used as a kinetic parameter. In order to determine the effect of molecular weight and type of polymer chain ends, three PPQ samples were prepared that differed only in molecular weight and polymer chain endgroups. The apparent activation energy of isothermal crosslinking was independent of molecular weight and chain endings. Its value of 60 kcal/mole is the same as that for the thermal degradation of PPQ (determined by isothermal weight loss measurements). The rates of change of T_g at a particular temperature, however, are a function of both molecular weight (at least for these polymers that do not have a sufficiently high molecular weight) and the type of polymer chain ends. It was observed that isothermally crosslinked PPQ gave a higher break point in the TGA curve and also an increased char yield at 800°C than the linear precursor.     

Correlation of Cooperatively Localized Rearrangement on the “Fluidized Domain” of Polymers to Their Nonexponentially Viscoelastic Behaviors at Double Aging Processes (I): A Set of Reduced Universal Equations on the Stress Relaxation Modulus and Creep Comp

Based on the structure of glass (or liquid) polymers consisting of α-domain, β-co-domain, and entanglement constituent chain networks, and the nonexponentially viscoelastic behavior, a “heterophase fluctuation” model was proposed. It was found that the dynamics of cooperative rearrangement on the “fluidized domain” has a great shear rate, domain size, and temperature dependences. When the shear rate, domain size, and temperature dependences were taken account into the cooperatively localized rearrangement on the fluidized domain by the degradation of primary α-domain and the reformation of secondary β-co-domain constituent chains. A new dynamic theory of cooperatively localized rearrangement on the fluidized domain constituent chains with different size and different network chain length during physical and mechanical aging was established. The total viscoelastic free en-ergy of deformation resulting from the change in conformations of α-domain, β-co-domain, crytallite, crosslinked, and trapped entanglement constituent chains during aging processes was calculated by the combining method of kinetics and statistical mechanics. The constitu-tive equations and reduced stress relaxation modulus and creep compliances for three types of polymers were also derived. Finally, two reduced universal equations on creep compliance and stress relaxation modulus with a non-linear and two nonexponential parameters α and β were theoretically derived from the dynamic theory and a statistically extended mode coupling theory for double aging effects of polymers was developed. Results show that the two reduced universal equations have the same form as Kohlraush-Williams-Watts (K-W-W) stretched exponential function. The nonlinearity and the nonexponentiality are, respectively, originated from the memory effects of nonthermal and thermal history. The correlation of nonlinearity, α and β to the aging time, aging temperature, and the mesomorphic structure of fluidized domains was also established.     

γ-Irradiation of polystyrene emulsions

Aqueous polystyrene emulsions were subjected to γ-irradiation at 30°C and 0.6 Mrad/hr dose rate. Analogy with water-soluble systems suggests that such conditions might suppress chain scission and favor crosslinking. The (extrapolated) infinite-dose gel content and gel-permeation analysis of the polymer in the pre-gel region indicate that the extent of chain scission was negligible. The G (crosslink) value obtained from the dose for incipient gelation and molecular weight variations in the pre-gel region is 0.051. Charlesby-Pinner plots were linear, but linearity cannot be construed as indicating that chain scission has produced an effective random molecular weight distribution. Our results are consistent with the conclusions that crosslinking events are random and directly proportional to dose. The probability that a given crosslink is effective in increasing the gel content decreases with dose past the incipient gel point, however, because of cyclization on preformed gel. The crosslink density/dose ratio is a decreasing function of dose in this range. Attempts to predict dose–gel relations with assumptions of various initial molecular weight distributions were unsuccessful, possibly because of the neglected influence of cyclization on the measured gel content.     

辐射交联顺-1,4-聚丁二烯的网络结构特性和力学性能

本文根据Flory的溶胀理论和橡胶弹性理论,考察了顺-1 4-聚丁二烯辐射交联产物的化学网络和物理缠结网络结构特性及其对固体力学性能的影响。结果表明,交联产物的物理缠结网络密度远远大于化学交联网络密度。随着辐照剂量的增大,化学交联密度增高,物理缠结数下降。探讨了交联、缠结密度与Mooney-Rivlin方程的常数项C_1和C_2的关系。C_1来自化学交联网络的贡献;C_2来自物理缠结的贡献。物理缠结网络主要贡献于交联物体在小形变下的起始弹性模量G_0;化学交联网络则主要贡献于交联物体在大形变下的非线性弹性,即断裂强度(?)_B。     

Properties of poly(vinyl chloride) crosslinked by new difunctional reagents

Alkaline and alkaline earth salts of either dimercaptans obtained by duplication of o-mercaptobenzoic acid with α, ω-diols or of o-mercaptobenzoic acid have been synthesized. Their efficiency has been studied with respect to induction time before change in melt viscosity and crosslinking rate assessed with Haake plasticorder equipped with a Rheomix 600 internal mixer. Then efficiency with respect to crosslinking was also characterized by the assessment of the insoluble fraction in tetrahydrofuran. Mechanical properties of uncrosslinked and crosslinked PVC were compared at different temperature through either static tests with high strain as creep and tensile tests or dynamic test in the elastic domain. Except for creep resistance, crosslinking does not improve mechanical properties of plasticized PVC at temperature lower than 80°C if insoluble fraction in tetrahydrofuran is lower than 100 % by weight. Because chemical crosslinking leads to the existence of two interpenetrated networks, a physical one and a covalent one, the temporary physical network governs the properties until the melting of ordered domains, whereas the covalent network governs the properties if temperature rises above the melting temperature of the crystalline populations. To improve mechanical properties of crosslinked PVC at room temperature, the crosslinking density of the covalent crosslinks must be higher than the density of physical crosslinks. Such a situation is reached if insoluble fraction in tetrahydrofuran becomes 100 % by weight.     

Network parameters for crosslinking of chains with length and site distribution

Polymer chains are crosslinked to form a network. The chains are polydispersed, with an arbitrary distribution of weight and functionality. Crosslinks may form in three different ways: direct coupling (homopolymerization), direct coupling with propagation, and coupling through copolymerization with small monomers. Various network parameters are calculated. We give computational formulae for gel point, weight fraction soluble, weight fraction pendant, weight fraction effective, concentration of effective junctions, concentration of effective network strands, and the entanglement trapping factor. These formulae give exact values for systems that previously have only been solved using simplifying approximations. Examples show that such simplification may lead to sizable errors in the computation of network parameters.     

The evolution of the viscoelastic retardation spectrum during the development of an epoxy resin network

The evolution of the viscoelastic behavior of an epoxy resin at various stages of curing has been followed with the changes in the retardation spectrum. The creep J(t) and recoverable creep compliance J_r(t) curves of the neat epoxy resin Epon l00lF (Shell) were determined at temperatures between 30 and 77°C. The viscosity decreased over 8 orders of magnitude as the temperature was increased. Specimens with eight stages of network development were prepared by reacting all of the epoxy resin's oxirane rings with amine hydrogens from varying ratios of a monofunctional amine (methyl aniline) and a tetrafunctional amine 4,4′-diamino diphenyl sulfone (DDS). Preparations in which 25, 35, and 40% DDS were used did not result in a molecular network, so they were viscoelastic liquids. With 45% DDS, the product had a nascent network and was judged to be just beyond the point of incipient gelation. The remaining preparations from 0.50, 0.60, 0.70, and 1.0 DDS yielded tighter less compliant molecular networks. The creep and recoverable compliance curves were measured over a range of temperatures above the glass transition temperature, T_g. They were reduced to T_g, and retardation spectra L(ln τ) were calculated.     

Influence of crosslinking on mechanical and dielectric properties of nitrile-butadiene-rubber

Several copolymers of acrylonitrile with butadiene (different acrylonitrile content, different molecular weight), uncrosslinked and crosslinked by tetramethylthiuramdisulfide or radiation, are investigated by dynamic mechanical measurements (10^–4 Hz to 100 Hz). The viscoelastic behaviour at very low frequencies is strongly influenced by molecular weight and crosslinking whereas the main relaxation (glass process) remains nearly the same. Stress strain curves (Mullins effect) and some dielectric measurements are also reported.     

Creep behavior of ultrahigh-modulus polyethylene: Influence of draw ratio and polymer composition

The creep behavior of ultrahigh-modulus polyethylene monofilaments has been studied over the temperature range 20–70°C. A wide range of samples was examined in an attempt to determine the influence of draw ratio, molecular weight, copolymerization, and crosslinking by γ irradiation Prior to drawing. Results are also presented for a solution-spun fiber. It is proposed that the permanent flow creep arises from a combination of two creep processes, one of which is associated with the crystalline regions of the oriented structure and the other with a molecular network.     

A statistical approach to characterize the viscoelastic creep compliances of a vinyl ester polymer

The objective of this study was to develop a model to predict the viscoelastic material functions of a vinyl ester (VE) polymer with variations in its experimentally obtained material properties under combined isothermal and mechanical loading. Short-term tensile creep experiments were conducted at three temperatures below the glass transition temperature of the VE polymer, with 10 replicates for each test configuration. The measured creep strain versus time responses were used to determine the creep compliances using the generalized viscoelastic constitutive equation with a Prony series representation. The variation in the creep compliances of a VE polymer was described by formulating the probability density functions (PDFs) and the corresponding cumulative distribution functions (CDFs) of the creep compliances using a two-parameter Weibull distribution. Both Weibull scale and shape parameters of the creep compliance distributions were shown to be time and temperature dependent. Two-dimensional quadratic Lagrange interpolation functions were used to characterize the Weibull parameters to obtain the PDFs and, subsequently, the CDFs of the creep compliances for the complete design temperature range during steady state creep. At each test temperature, creep compliance curves were obtained for constant CDF values and compared with the experimental data. The predicted creep compliances of the selected VE polymer in the design space are in good agreement with the experimental data for all three test temperatures.     

Solid polymer electrolytes I,preparation, characterization,and ionic conductivity of gelled polymer electrolytes based on novel crosslinked siloxane/poly(ethylene glycol) polymers

A series of crosslinked siloxane/poly(ethylene glycol) (Si–PEG) copolymers were synthesized from the reactive methoxy‐functional silicone resin (Si resin) and PEGs with different molecular weights via two kinds of crosslinking reactions during an in situ curing stage. One of the crosslinking reactions is the self‐condensation between two methoxy groups in the Si resin, and another one is an alkoxy‐exchange reaction between the methoxy group in the Si resin and the OH group in PEG. The synthesized crosslinked copolymers were characterized by Fourier transform infrared spectroscopy, DSC, and ¹³C NMR. The crosslinked copolymers were stable in a moisture‐free environment, but the Si? O? C linkages were hydrolyzed in humid conditions. The gel‐like solid polymer electrolytes (SPEs) were prepared by impregnating these crosslinked Si–PEG copolymers in a propylene carbonate (LiClO₄/PC) solution. The highest conductivity reached 2.4 × 10^?4 S cm^?1 at 25 °C and increased to 8.7 × 10^?4 S cm^?1 at 85 °C. The conductivities of these gel‐type SPEs were affected by the content of LiClO₄/PC, the molecular weights of PEGs, and the weight fraction of the Si resin. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2051–2059, 2004     

Photocrosslinking of polyethylene. II. Properties of photocrosslinked polyethylene

Some properties of photocrosslinked high density polyethylene (2 mm thick sheets) have been studied. The homogeneity of the network is greatly improved by the application of triallylcyanurate (TAC) as crosslinking agent. The role of TAC in promoting the crosslinking is discussed. The crosslinked PE is found to be durable towards immersion in boiling water. Oxygen permeability increases while density and melting point decrease with increasing degree of crosslinking. The network chain density is obtained using conventional swelling method in boiling xylene, which together with data from melting point depression show that contribution of chain entanglement is insignificant to the gel formation of PE in this work.     

Chain entanglement and viscoelastic properties of molten polymers

Linear low-density polyethylenes (LLDPES) and polypropylene (PP) have been recovered from solutions of varying initial polymer concentration. Melts of these polymers show significant reductions in viscosity and elasticity, and the effects are attributed to changes in the entanglement density of the polymer. Measurements of entanglement densities have been attempted from experimental values of the apparent zero-shear melt viscosity. These indicate that solution treatments in trichlorobenzene at 135°C reduce the entanglement density more effectively in PP than in LLDPE. In all cases the observed effects are reversible by annealing at elevated temperatures. Analytic data point to entanglement changes as the true origin of changes in viscoelastic properties, since solution treatments produce no changes in molecular weights and weight distributions, and the samples tested are free of solvent residues.     

Molecular weight relations for crosslinking of chains with length and site distribution

Many polymer networks are formed by crosslinked polymer chains through reactive sites distributed along the chains. How these sites are distributed as well as the chain length distribution can have a significant effect on properties like the gel conversion and molecular weight. Previous treatments have used simplifying approximations. In this paper we eliminate these approximations and derive computational formulae for weight average molecular weight and gel point for polymer chains of any length and reactive site distribution. Three types of crosslinking are considered: direct coupling of chains (homopolymerization), direct coupling through propagation, and coupling through copolymerization with small monomers.     

Crosslinking Kinetics: Partitioning According to Number of Crosslinks

Summary: To mathematically describe crosslinking kinetics for polymers, we have proposed a novel method that accounts for the number of crosslinks, that is, partitioning according to number of crosslinks (PANC). By contrast, the well‐known method of numerical fractionation tracks generations of crosslinked molecules, defined to include a range of crosslinks. The proposed crosslinking kinetics yield a population balance model that provides moments and hence measurable average properties such as number average molecular weight and weight average molecular weight, polydispersity and average crosslink number. The gel points for batch and continuous‐flow stirred‐tank reactors are derived. Because the usual closure methods do not yield satisfactory convergence, new representations for post‐gelation moments are proposed. The results realistically show how the moments change with time in the post‐gel region.

The average number of crosslinks in the bulk and sol versus time in a batch reactor; the gel point is the dashed line.