Ultimate tensile properties of elastomers. VII. Effect of crosslink density on time–temperature dependence

Data on tensile strength and elongation at break for a series of Viton A-HV vulcanizates are discussed. The data were obtained at various extension rates at temperatures from ?5 to 230°C (25 ? T — T_g ? 260°C) on seven vulcanizates having crosslink densities v_e (estimated from C₁ in the Mooney-Rivlin equation) from 0.46 × 10^?5 to 24.4 × 10^?5 mole/cm³. At an extension rate of 1 min^?1, an increase in v_e affects the tensile strength σ_b (based on the undeformed cross-sectional area) and the true tensile strength σ_bσ_b (based on the cross-sectional area of a deformed specimen) as follows: σ_b is essentially constant at a low temperature; it passes through a decided maximum at intermediate temperatures; and it increases to a plateau at elevated temperatures. In contrast, λ_bσ_b decreases markedly at all temperatures, an exception being the most lightly crosslinked vulcanizate(s). Application of time—temperature superposition to the ultimate-property data gave log a_T; its temperature dependence is that typical of nonpolar rubbery polymers. Data on the vulcanizates were compared in corresponding temperature states by plotting log 273σ_b/T, log 273λ_bσ_b/T, and (λ_b — 1)/(λ_b — 1)_max against logt_b/(t_b)_max, where t_b is the temperature-reduced time to break and (t_b)_max is the value at which the ultimate extension ratio λ_b attains its maximum, (λ_b)_max. Except for the most lightly crosslink vulcanizate, the comparison shows that 273λ_bσ_b/T and (λ_b — 1)/(λ_b — 1)_max are substantially independent of (or only weakly dependent on) crosslink density, that 273λ_b/T increases with v_e, and that 273λ_b/T ∝? v_e^0.6 and λ_b ∝? v_e^?0.4 at a large value of t_b/(t_b)_max.     

Effect of finite extensibility on the viscoelastic properties of a styrene–butadiene rubber vulcanizate in simple tensile deformations up to rupture

Stress–strain and rupture data were determined on an unfilled styrene–butadiene vulcanizate at temperatures from ?45 to 35°C and at extension rates from 0.0096 to 9.6 min^?1. The data were represented by four functions: (1) the well-known temperature function (shift factor) a_T; (2) the constant strain rate modulus, F(t,T), reduced to temperature T₀ and time t/a_T, i.e., T₀F(t/a_T)/T; (3) the time-dependent maximum extensibility, λ_m(t/a_T); and (4) a function Ω(χ) where χ = (λ ? 1)λ_m⁰/λ_m, in which λ is the extension ratio and λ_m⁰ is the maximum extensibility under equilibrium conditions. The constant strain rate modulus characterizes the stress–time response to a constant extension rate at small strains, within the range of linear response; λ_m is a material parameter needed to represent the response at large λ; and Ω(χ) represents the stress–strain curve of the material in a reference state of unit modulus and λ_m = λ_m. The shift factor a_T was found to be sensibly independent of extension. At all values of t/a_T for which the maximum extensibility is time-independent, the relaxation rate was also found to be independent of λ. These observations indicate that the monomeric friction coefficient is strain-independent over the ranges of T and λ covered in the present study. It was found that λ_m⁰ = 8.6 and that the largest extension ratio at break, (λ_b)_max, is 7.3. Thus, rupture always occurs before the network is fully extended.     

Thermomechanical behavior of rubberlike materials

A simple form of nonisothermal free energy function A(λ₁, λ₂, λ₃, T) for rubberlike materials results from postulating that the entropy is a separable symmetric function of the extension ratios λ_i along the principal strain directions and considering the fundamental properties of rubberlike materials, i.e., that rubber elasticity is associated primarily with changes in entropy and the variation of elastic tension with changes in temperature is linear. The explicit representation of A is reduced to the Valanis-Landel strain energy function for isothermal cases.     

Uniaxial and biaxial stretching of silicone putty

Two novel experimental methods are used. Vertical uniaxial stretching is obtained by attaching a perspex rod to the lower end of a silicone putty cylinder; the rod then descends into water of constant depth. The stress and rate of extension change little during each test, but the rate of extension may be varied from 0.005 to 0.10 s⁻¹ by modifying the experimental conditions. Biaxial stretching is acchieved by placing a disc of silicone putty across the top of an open glass cylinder which is lightly pressurized. The sample expands as a spherical cap, the height of the centre above the cylinder being timed. The stress in the cap passes through a shallow minimum as it expands (at constant pressure) and the slowly varying rate of biaxial extension may be readily determined. This lies in the range 0.003–0.06 s⁻¹. For low rates of uniaxial or biaxial extension, it is possible to plot the extension against time and to show how the extensional viscosity varies with the strain rate (or principal extension ratio). For high rates of extension, a ‘single point’ determination of the extensional viscosity may be made, with the stress and strain rate averaged at the mid-point of the sample's extension. The temperature is 26.5 ± 1.5 °C. The following is shown under the experimental conditions:(a) the extensional viscosity (uniaxial or biaxial) is in the range 1.0 × 105 to 3.0 × 10⁵ Pa s;(b) for extensional strain rates between 0.01 and 0.04 s⁻¹, the uniaxial and biaxial extensional viscosities are of comparable value;(c) both forms of the extensional viscosity tend to decrease with increased extensional strain rate, the biaxial extensional viscosity falling more rapidly and being higher than the uniaxial viscosity at low strain rates and lower at high strain rates;(d) there are no signs of rupture in uniaxial extension (principal extension ratios up to 1.8 and extensional strain rate up to 0.1 s⁻¹);(e) in biaxial extension, the sample tends to rupture more easily as the strain rate is increased. (The sample fails at the principal extension ratio of 2.0 at an extensional strain rate of 0.02 s⁻¹ and fails at a principal extension ratio of 1.3 at an extensional strain rate of 0.07 s⁻¹.)     

Failure analysis of plain woven glass/epoxy laminates: Comparison of off-axis and biaxial tension loadings

An experimental study was focused on investigation of the failure properties of plain woven glass/epoxy composites under off-axis and biaxial tension loading conditions. Four fibre orientations (0°, 15°, 30° and 45° with respect to the load direction) were considered for off-axis tests and two biaxial load ratios for biaxial tests to study failure characteristics and mechanism. Four classical polynomial failure criteria - Tsai-Hill, Hoffman, Tsai-Wu and Yeh-Stratton - were analysed comparatively to predict off-axis and biaxial failure strength of the composites. For failure prediction of the plain woven composites under multiaxial tension loads, the Tsai-Wu criterion was modified by introducing an interaction coefficient F₁₂ obtained from 45° off-axis or biaxial tension tests and the Yeh-Stratton criterion was modified with the interaction coefficient B₁₂ = 0 or obtained from the biaxial tension test. The former criterion was found to have higher accuracy. Finally, according to macroscopic and microscopic studies, the failed specimens showed mostly distinct failure with a specific fracture orientation, mainly exhibiting fibre or fabric tensile fracture mode and a combination of matrix cracking and delamination, both in off-axis and cruciform samples.     

Reaktionen von tricarbonyl-chrom-η6λ3-phosphorin-komplexen zu tricarbonyl-chrom-η6λ5-phosphorin-ylid-komplexen

The tricarbonylchromium η⁶π⁶ complexes of 2,4,6-triphenyl- and 2,4,6-tri-t-butyl-λ³-phosphorins 3a and 3b add nucleophiles regio- and stereo-specifically to the phosphorus atom in the exo-position giving the λ⁴-phosphorin anions which now add electrophiles in the endo position, giving η⁵π⁶-λ⁵-phosphorin ylide complexes 5a and 5b, respectively. The ¹H, ¹³C and ³¹P NMR spectra of 3a and 3b and especially 5a and 5b are discussed with respect to the stereoisomeric complexes 5a having two different exocylic substituents at the phosphorus atom, synthesized from e.g. 1-ethyl-1-methyl-2,4,6-triphenyl-λ⁵-phosphorin and Cr(CO)₆. The tricarbonylchromium-1,1,-dialkyl or alkyl-aryl-2,4,6-tri-t-butyl-λ⁵-phosphorin 5b can only be synthezised from tricarbonylchromium-2,4,6-tri-t-butyl-λ³-phosphorin by addition of nucleophiles and electrophiles since the corresponding λ⁵-phosphorin derivatives are not available. By removal of the tricarbonylchromium residue from the λ⁵-phosphorin-ylide complexes 5b, however, also 2,4,6-tri-t-butyl-λ⁵-phosphorins can be prepared.     

Strain hardening of high density polyethylene

The introduction of true stress strain measurements, at constant strain rate, has promoted the development of empirical or semiempirical models for large deformations in thermoplastics. One such theory, which proposes that the post yield deformation process can be represented by equations derived from the theories of rubber elasticity, has been successfully applied to several glassy polymers. Unexpectedly, it can also model the post yield deformation of many different grades of polyethylene, even when rubber theory is employed in the simplest Gaussian form. Strain hardening is then represented by the single strain hardening coefficient Gp. Examples are given of this equation, which can be modified to give the true engineering or nominal stress σ_n and then be differentiated to give dσ_n/dλ = Gp ? Y₀ / λ² + 2Gp / λ³, where Y₀ is the yield stress and λ the extension ratio. Negative values of this differential then predict the onset of necking in tension and positive values stabilization of the neck. The relation of Gp to molecular weight is then discussed using literature measurements for polyethylenes of differing molecular weight and similar molecular weight distributions. When these results are then plotted, a strong dependency of Gp on molecular weight is observed. Some implications of these measurements are then considered. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1090–1099, 2007     

Effect of molecular entanglements on craze microstructure in glassy polymers

Thin films of ten glassy polymers are bonded to copper grids and strained in tension to produce crazes, which are then examined in the transmission electron microscope. The average craze fibril extension ratio λ for each polymer is determined from microdensitometer measurements of the mass thickness contrast of the crazes. The extension ratio λ is found to increase approximately linearly with the chain contour length l_e between entanglements, as determined from melt elasticity measurements of the entanglement molecular weight of these polymers. These results are analyzed by comparing them with λ_max, the maximum extension ratio of an entanglement network in which polymer chains neither break nor reptate (i.e., permanent entanglement crosslinks are assumed). The values of λ_max are given by l_e/d where d, the entanglement mesh spacing in the unoriented glass, is computed from d = k(M_e)^1/2 with k determined either from small-angle neutron scattering results on isolated chains in the glass or from coil size measurements in dilute solutions of a θ solvent. The craze extension ratios fall somewhat below λ_max at low λ but increase to well above λ_max for polymers with high l_e. This comparison suggests a significant contribution due to chain breakage (or reptation) in the higher-λ crazes of large-l_e polymers, which may arise from the higher true stresses in the craze fibrils (which for a given applied stress increase proportionally to λ). The results also imply that a useful way to increase the “brittle” fracture stress and decrease the ductile-to-brittle transition temperature of a glassy polymer is to decrease its entanglement contour length l_e.     

Mechanical properties of natural rubber vulcanizates in finite deformation

Mechanical properties of four kinds of natural rubber vulcanizates differing in vulcanization conditions, and consequently in degree of crosslinking (having values of the Mooney-Rivlin constant C₁ ranging from 0.68 to 1.98) were observed under orthogonal biaxial stretching in a range of strain invariants I_i from 3.4 to 9.0 (extension ratios λ_i from 0.7 to 3.0). The results obtained were analyzed by two methods. One method employed the Valanis-Landel postulate that the strain-energy function W(λ₁, λ₂, λ₃) is a separable symmetric function of the principal extension ratios, i.e., W(λ₁,λ₂,λ₃) = w(λ₁) + w(λ₂) + w(λ₃); the other utilized the contour plots of ?W(I₁, I₂)/?I₁ and ?W(I₁, I₂)/?I₂ surface within the (I₁, I₂) domain. The postulate for W was examined in detail with good agreement with experimental results. The dependences of ?W(I₁, I₂)/?I₁ and ?W(I₁, I₂)/?I₂ surfaces on the degree of crosslinking and temperature were further investigated, with the following conclusions. The surfaces have fairly steep slopes for the region of relatively small deformation (i.e., I₁ < 5) and become flat with increasing I_i for all the test specimens. The slope becomes less steep with decreasing degree of crosslinking. The values of ?W/?I₁ increase linearly and the ?W(I₁,I₂)/?I₂ surface becomes flat, both with increasing temperature: i.e., the temperature dependence of ?W/?I₁ further depends on I_i. The ?W(I₁,I₂)/?I₂ surface has a maximum near 40°C.     

Conformational analysis of asymmetric ethanes : Extraction of acyclic conformational ligand constants from time-averaged geminal fluorine anisochronism

The syntheses and ambient-temperature ¹⁹F NMR data are reported for 27 asymmetric ethanes of the general formula RCF₂CXYZ, including a complete series of 10 compounds with R = Cl and all combinations of the 5 ligands H, F, Cl, Br and Ph. Within the theoretical framework of a previously proposed heuristic mathematical model the geminal ¹⁹F chemical shift differences are fitted to chirality functions X = ?R (λx - λy) (λy - λz) (λz - λx) to yield acyclic conformational ligand constants λ and substituent parameters ?. It is demonstrated that the λ constants already reported for an analogous series of 10 compounds with R = Br are transferable to the Cl series with ?_Cl = 0.63 ± 0.07. Crude first approximations are also reported for the normalised (according to ?_Br = 1) ligand constants λ_Ch3, λ_OH, λ_OCH3 and λ₁ and for the substituent parameter λ_H. It is argued that the λ values thus ext play a role in the conformational analysis of asymmetric ethanes that is conceptually analogous to the conformational free energies in monosubstituted cyclohexanes.     

An x-ray pole figure analysis on biaxially deformed polyethylene film

The orientational states induced upon two-step biaxially stretching low-density polyethylene at 25°C have been investigated. A pole figure analysis of the (200), (020), and (002) crystalline planes has been employed to elucidate the evolution of the molecular crystalline orientation as a function of biaxial stretching. The initial uniaxial-like orientation induced along the extrusion direction of the films was gradually lost upon transverse stretching and, consequently, replaced by a biaxial orientation as suggested by the orientation functions. In these cases, the a crystallographic axis was observed to be strongly oriented along the film normal, thus confining the c and b axes to the film plane. The pole figures clearly indicate that the c and b axes are preferentially aligned 45° with respect to the stretching directions. This unique orientational state of the orthorhombic unit cell of polyethylene has been termed a biaxial-double orientation. Birefringence measurements on the biaxial samples indicated that the amorphous and crystalline regions are simultaneously biaxially oriented. The evolution of the crystalline orientation as a function of stretching was conveniently followed on a White/Spruiell orientation triangle. Quantification was hindered, however, by the presence of different crystal populations in the biaxially stretched samples. © 1994 John Wiley & Sons, Inc.     

Ultradrawing of high-molecular-weight polyethylene cast from solution. II. Influence of initial polymer concentration

Ultradrawing of films of high-molecular-weight polyethylene (M?_w = 1.5 × 10⁶) produced by gelation crystallization from solution is discussed. The influence of the initial polymer volume fraction (?) on the maximum draw ratio (λ_max) of the dried films is examined in the temperature region from 90–130°C. The results can be described very well by the relation λ_max = λ ?^?1/2 where λ is the (temperature-dependent) maximum draw ratio of the melt-crystallized film. An attempt is made to discuss the marked influence of the initial polymer volume fraction on λ_max in terms of the deformation of a network with entanglements acting as semipermanent crosslinks.     

Entanglement networks of 1,2-polybutadiene crosslinked in states of strain. VII. Stress-birefringence relations

Crosslinks are introduced by γ irradiation into 1,2-polybutadiene while strained in uniaxial extension near T_g with stretch ratio λ₀, thereby trapping a proportion of the entanglements originally present. The stress at any subsequent strain λ is accurately given by the sum σ_N + σ_x, where σ_N is the stress contributed by a trapped entanglement network with λ = 1 as reference and a Mooney–Rivlin stress-strain relation, and σ_x is that contributed by a crosslink network with λ = λ₀ as reference and neo-Hookean stress-strain relation. The birefringence is accurately given as δn = ?_Nσ_N + ?_xσ_x, where the ?'s are the respective stress-optical coefficients. From measurements at λ = λ₀ where σ_x = 0, ?_N can be determined separately. For polymer with 88% 1,2 microstructure, ?_N and ?_x are nearly equal and independent of irradiation dose, though strongly dependent on temperature. For polymer with (95–96)% 1,2, ?_N and ?_x are different (even opposite in sign) and dependent on dose. This behavior is associated with a side reaction of cyclization by the γ irradiation, which is inhibited by the 1,4 moiety in the polymer with lesser 1,2 content. It is responsible for residual birefringence in the state of ease (λ = λ_s) where σ_N = –σ_x and the stress is zero.     

Luminescent nitro derivatives of benzotriazolo[2,1a]benzotriazole

Fluorescence was enhanced and laser activity introduced by substitution in 5,11-dehydro-5H,11H-benzotriazolo[2,1-a]benzotriazole 6 to give 2-nitro, 2,8-dinitro, 2,4,8-trinitro, and 2,4,8,10-tetranitro derivatives 9a–d . Luminescence for compounds 6 and 9a–d and the 2,8-dinitro-3,9-dimethyl and 2,3,8,9-tetramethyl-4,10-dinitro derivatives 11a,b was erratically solvent dependent when examined in ethyl acetate, acetonitrile, and acetone and was most efficient in the 2,8-dinitro derivative 9b [λ_f 479 nm (ethyl acetate) Φ 0.98, λ_f 501 nm (acetonitrile) Φ 0.58, and λ_f 494 nm (acetone) Φ 0.61] and in the tetranitro derivative 9d [λ_f 509 nm (acetonitrile) Φ 0.81 and λ_f 511 nm (acetone) Φ 0.66]. With laser activity at 560–590 nm (acetonitrile) the dye 9b was 30% as efficient as rhodamine 6G (ethanol) in power output. Luminescence was quenched by the reduction of nitro groups to give 2-amino and 2,8-diamino derivatives 9e,f and by the conversion of the tetranitro compound 9d to an unassigned diazido dinitro derivative 9g . Luminescence was not detected in 2,5-dimethyl-3,6-dinitro-1,3a-4,6a-tetraazapentalene 14 and ethyl 2,5-dimethyl-1,3a,4,6a-tetraazapentalene-3,6-dicarboxylate 15 . Azidoazobenzenes were obtained from 4-methyl- and 4,5-dimethyl-1,2-phenylene diamines via oxidation with lead dioxide to aminoazobenzene derivatives followed by treatment of the diazotized amines with sodium azide and thermolysis of azido intermediates to give 3,9-dimethyl and 2,3,8,9-tetramethyl derivatives 10a,b of the triazolotriazole 6 . Nitration converted the triazole 6 to the 2,4,8-trinitro derivative 9c and the alkyltriazoles to their dinitro derivatives 11a,b .     

Application of a new structural theory to polymers. I. Uniaxial stress in crosslinked rubbers

A continuum rheological theory, endowed with generalized structural significance, has recently been developed. Based on nonequilibrium thermodynamics, it relates stress σ, strain rate \documentclass{article}\pagestyle{empty}\begin{document}$\dot \varepsilon$\end{document} and temperature in terms of material evolution through a series of structural states. The theory has previously had success in dealing with crystalline metals and surface physics, and here it is applied to crosslinked rubbery polymers in the nominally amorphous condition. Structure is believed to be related to interchain associations, chain entanglements, chain ends, and other defects in the hypothetical ideal network which by itself would lead to neo-Hookean predictions in uniaxial deformation, σ^nH ∝ λ² — λ^?1, where λ is the stretch ratio. Predictions are made for σ(λ) in both tension and compression and shown to be more compatible with data than either σ^nH(λ) or the Mooney—Rivlin expression σ^MR(λ). Only two parameters are required, moduli G_o (reflecting initial structure) and G_s (the steady-state condition), and rate effects are incorporated through G_o(\documentclass{article}\pagestyle{empty}\begin{document}$\dot \varepsilon$\end{document}) and G_s(\documentclass{article}\pagestyle{empty}\begin{document}$\dot \varepsilon$\end{document}). The phenomena of yielding and stress softening in cyclic tensile loading are also predicted, suggesting advantages to this approach relative to conventional viscoelastic continuum models.     

Effect of surface swelling on diffusion on polymers. II. Delamination

Swelling in chloroform resulted in delamination of surface-hydroxylated styrene-butadiene-styrene block copolymers, with the formation of three fractions: crosslinked gel, reacted sol, and unreacted chloroform-soluble material. From the relative weights of these fractions, the depth of penetration of the reaction and the shape of the reaction front were determined. The weight of the gel fraction gave directly an estimate of the depth of penetration, λ_x which decreased with increasing film thickness. This was attributed to the increased amount of reacted polymer being noncrosslinked material (sol) in the interior compared to the 100% crosslinked nature of the surface region and to a reduction in the penetration of the reaction front resulting from the effect of stress transfer in lowering the permeation rate of peracetic acid. Comparison of the depth of penetration estimates λ_x and λ_s determined from the weight of the unreacted polymer demonstrated that, for the conditions used, the reaction front is quite broad. (For example, at 40°C, in 71% acetic acid for 80 min, the fully crosslinked portion is 15 μm thick and the partially reacted region extends for another 8.5 μm.) The combined influences of the increase in penetration of the reactants in the polymer and the relief of stress secondary to this increase in penetration were reflected in the time dependence of the depths of penetration λ_x and λ_s.     

Some observations on the reaction of cysteine with o-phthalaldehyde

Cysteine can behave simultaneously as an amino compound and thiol in the reaction with o-phthalaldehyde to produce a fluorescent compound. At room temperature, no reaction is observed, but a very stable compound (λ_exc = 364 nm, λ_em = 424 nm) is slowly formed upon heating. Constant fluorescence intensity is achieved after heating at 50°C for 3 h, remaining unchanged for at least 3 h when cooled.     

Nonlinear relaxation of stress and birefringence in simple extension of 1,2-polybutadiene

Relaxation of stress and birefringence in simple extension has been studied for two samples of 1,2-polybutadiene with 95% and 88% vinyl content and weight-average molecular weight 1.9 and 2.9 × 10⁵, respectively. The extension ratio, λ, ranged from 1.14 to 2.08, temperatures from 0 to 15°C, and times, reduced to 0°C, up to 3 × 10⁵ sec. The stress-optical coefficient C was negative and positive, respectively, for the two samples, the difference being attributable to opposite signs and very different magnitudes of the contributions of the 1,2 and 1,4 moieties to the birefringence. For each polymer, C was independent of time but increased (algebraically) with temperature. For one polymer a very minor dependence of C on λ was observed. At any instant of time, the dependence of both stress and birefringence on λ could be described by equations of the Mooney–Rivlin form with coefficients C₁,C₂ and B₁,B₂, respectively. At short times the contributions of the C₁ and C₂ terms to the stress and of the B₁ and B₂ terms to the birefringence are roughly equal. With increasing time, C₁ and B₁ decrease gradually while C₂ and B₂ remain constant over several decades in time. Finally, C₂ and B₂ decrease rather rapidly. A tentative interpretation of these phenomena in terms of motions of entanglements is given.