Relaxation of shear and normal stresses in step-shear deformation of a polystyrene solution. Comparison with the predictions of the Doi–Edwards theory

The shear stress σ, two components of birefringence, and extinction angle were measured for a concentrated polystyrene solution in step-shear deformation of magnitude of shear 0.3 ≤ γ ≤ 4.0. The stress-optical coefficient did not depend on either γ or time. The first and the second normal-stress differences v₁ and v₂ were evaluated with the use of the stress-optical law. Over a certain range of long times, σ could be factored as σ = γh(γ)G(t) and the quantity h(γ) agreed with the prediction of the Doi–Edwards theory based on the de Gennes tube model of entangled polymer chains. At short times the effect of γ on σ/γ was smaller than at long times. The relaxation spectrum became approximately independent of γ at the short-time end of the rubbery plateau region. The ratios v₁/σ and v₂/v₁ were independent of time and were in quantitative agreement with those predicted by the Doi–Edwards theory: v₁/σ was equal to γ, v₂/v₁ was negative, and |v₂/v₁| decreased with increasing γ.     

Birefringence of polyethylene melt in transient elongational flow at constant strain rate

Simultaneous birefringence and elongational viscosity measurements were carried out on molten commercial grade, low-density polyethylenes during simple elongational flow at constant strain rate and constant temperature. The birefringence increased with time during constant strain rate elongation. The increase in birefringence was a linear function of elongational stress throughout whole elongation, but the elongational viscosity increased in two stages. The increase in elongational viscosity can be divided into linear viscoelastic and nonlnear viscoelastic regions. The linear region appeared at small strain and the nonlinear region appeared at strain greater than 0.7. The elongational viscosity in the nonlinear region increased much more rapidly than that in the linear region. The Gaussian approximation, which is commonly used in molecular models, could be used for the transient elongational flow. A constant stress-optical coefficient C = 1.3 × 10^?10 cm²/dyn was obtained for all the elongational experiments, independent of strain rate (0.002-0.2s^?1). The stress-optical coefficients were weakly dependent on temperature, as predicted by the theory of rubber elasticity.     

Effect of shear history on the steady shear flow behavior of a thermotropic liquid-crystalline polymer

The steady shear stress (σ) and first normal stress difference (N₁) of a thermotropic liquid-crystalline polyester, poly[(phenylsulfonyl)-p-phenylene 1,10-decamethylene-bis(4-oxybenzoate)] (PSHQ10), in both the isotropic and nematic regions were measured as a function of shear rate (γ), using a cone-and-plate rheometer. For the study, PSHQ10 was synthesized via solution polymerization in our laboratory. The PSHQ10 was found to have (a) the weight-average molecular weight of 45,000 relative to polystyrene standards and a polydispersity index of 2, (b) a glass transition temperature of 88°C, (c) a melting point of 115°C, and (d) a nematic-to-isotropic transition temperature of 175°C. For the measurements of σ and N₁ in the nematic region of PSHQ10, its initial conditions for the startup of shear flow was controlled by (a) first heating an as-cast specimen to 190°C, (b) shearing there at γ = 0.085 s^?1 for about 5 min, and then (c) cooling slowly down to a predetermined temperature (130, 140, 150, 160, or 171°C) in the nematic region. For each γ chosen, after start-up of shear flow, we waited for a sufficiently long time until both the shear stress and first normal stress difference leveled off, giving rise to steady-state values of σ and N₁. Emphasis was placed on investigating the effect of shear history on σ and N₁ of PSHQ10 in the nematic region. For this, the following experiments were conducted: (a) a fresh specimen was sheared continuously by increasing the γ stepwise, and (b) a presheared specimen was further sheared continuously by increasing the γ stepwise. We have found that fresh specimens exhibited ‘shear-thinning’ behavior over the entire range of γ (0.008?0.27 s^?1) tested, whereas the presheared specimens exhibited both zero-shear viscosities and shear-thinning behavior. When using fresh specimens, we found that N₁ was positive over the entire range of γ (0.008–0.27 s^?1) tested. However, when using presheared specimens we found that (a) at very low γ, N₁ initially was negative and then became positive as shearing continued, and (b) at higher γ, N₁ was positive over the entire duration of shearing. © 1994 John Wiley & Sons, Inc.     

Random-coil configurations of aromatic polyesters: Stress-optical behavior of poly(diethylene glycol terephthalate)

The stress-optical behaviour of an elastomeric network of poly(diethylene glycol terephthalate) (PDET) was measured over a wide range of elongation ratios α (up to 5) and temperatures (293-353K). No evidence of strain -induced crystallization was found;on the contrary, the plot of birefringence versus stress exhibits negative deviations from linearity at values of α over 2.6. Values of the optical configuration parameter Δα of the order of 20 × 10^?24cm³ with relative temperature coefficients of -1.1 × 10^?3K^?1 were found for the unswollen sample. The introduction of tricresylphosphate as diluent roughly doubles the birefringence of the network, presumably because of an increase in intermolecular interactions. Theoretical calculations carried out with the RIS model give values of Δα about one order of magnitude smaller than the experimental ones and temperature coefficients of about 4.1 × 10^?3K^?1. No reasonable modification of conformational energies or contributions to the anisotropic part of the polarizability tensor would achieve agreement between theory and experiments. The discrepancy between theoretical and experimental results may be qualitatively explained by intermolecular interactions.     

Birefringence of amorphous polyoxides: Stress-optical behavior of poly(3-methyltetrahydrofuran)

The stress-optical behavior of an unswollen elastomeric network of poly(3-methyltetrahydrofuran) was measured for elongation ratios a in the range 1.182–1.549, at several temperatures between 20 and 60°C. No evidence of strain-induced crystallization was found; moreover, the dependence of birefringence Δn on true stress f/A was linear in the interval of α investigated. Values of Δa ranged from 2.4 to 2.8 in units of 10^?24 cm³, in the temperature range studied, with a temperature coefficient 3.1 × 10^?3 K^?1. Theoretical calculations carried out with the rotational-isomeric-state model gave values of Δa noticeably smaller than the experimental results; however, a small increase in the backbone valence angles θ improved the theoretical result of Δa without worsening that of the dipole ratio. Analysis of the Δa results seems to corroborate the conclusion obtained through the study of dipole moments concerning the preference for nucleophilic attack on the less hindered α carbon in the monomer. Theoretical and experimental values of the temperature coefficient of Δa were in clear disagreement; a qualitative explanation for this discrepancy is discussed.     

Membrane Permeability and Stability of Liposomes Suspended in Shear Flow

The 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) liposome has been characterized in its stability and membrane permeability to 5(6)-carboxyfluorescein (CF) in the shear flow generated in the cone-and-plate geometry. The CF-containing liposomes (CFLs) were 101–323 nm in the mean diameter D _P as measured with the dynamic light scattering (DLS) method. Adsorption of lipids to the cone-and-plate was observed, which clearly depended on the shear stress applied at the shear rate γ up to 1.5 × 10³ s^?1. The permeability of CFLs with D _P of 101 and 117 nm definitely increased at the maximum γ value where the adsorption was negligible. The permeability coefficient of CF at 40°C in the shear flow was 5.7 times larger than that in the static liquid system. The DLS measurements revealed that the size distribution of CFLs with D _P of 101–189 nm was practically unchanged under the shear stress even at 55°C. The results obtained show that the shear stress can permeabilize the CFL membranes with neither structural collapse nor coalescence.     

Stress-optical properties of poly(oxypropylene) networks

Strain birefringence of poly(oxypropylene) was studied using several poly(oxypropylene) model networks of different crosslink densities. Most of the measurements were carried out in elongation, in both the unswollen and the swollen states, over the temperature range 10–70°C. The optical configuration parameter was found to be Δa = (4.33 ± 0.09) × 10^?24 cm³ at 25°C with a very small temperature coefficient. Theoretical calculations based on rotational isomeric state theory were employed to interpret the experimental data. The results indicate the intermolecular correlations to be low for this polymer, and, contrary to other systems, the stress-optical coefficient C decreased with increasing average molecular weight between crosslinks. This fact was attributed to the end-group effect introduced by the crosslinking agent.     

Studies on biaxial stretching of polypropylene film. IV. Overall orientation during one-step biaxial stretching and its application to the estimation of the principal refractive indices of isotactic polypropylene

Polypropylene film was biaxially stretched in one step in air at 140°C or 152°C, and the deformation was studied optically. A linear relation held between Δn_ss and v_A^?½ for v_A > 10, at both temperatures, where Δn_ss is the birefringence with respect to the normal to the film and v_A is the degree of stretching expressed as the factor by which the area of the film is increased. Extrapolation of data in this linear region yielded a value of 20 × 10^?3 for ?Δn_ss at infinite v_A. Since it is presumed that the polypropylene molecules lie completely parallel to the film surface when the film is stretched infinitely, ?Δn_ss at v_A^?½ = 0 must be just half Δn°, the intrinsic birefringence in the case of completely parallel orientation. Thus, Δn° must be 40 × 10^?3. This value was obtained experimentally in uniaxial stretching when the birefringence with respect to the direction of drawing was extrapolated to infinite extension. Similar relations held between n_p, the average of the refractive indices in the two stretching directions, and v_A, and between n_ss, the index normal to the film, and v_A. By similar extrapolations, (1/2)(n′_γ + n′_β) and n′_β = n*_α′ were estimated, and thence nα′ was obtained. Here, n′_α and n′_β are the refractive indices along the c axis (molecular chain axis) and b axis. All these optical parameters refer to a density of 0.900 g/cm³. Hence by applying a density correction to those values, the principal refractive indices and the intrinsic birefringence of polypropylene crystal were evaluated as follows: n_α = 1.5522, n_β = n*_α = 1.5106 and Δn_c° = 4.16 × 10^?3, where n*_α is the refractive index prependicular to the b and c axes of the crystal.     

Crazing and shear deformation in crosslinked polystyrene

Thin films of polystyrene (PS) are bonded to copper grids and crosslinked with electron irradiation. When the films are strained in tension regions of local plastic deformation, either crazed or plane stress deformation zones (DZs), nucleate and grow from dust particles. the nature of the local deformation, as well as the local extension ration λ, is determined by transmission electron microscopy. The behavior of the PS glass is consistent with its being a network of molecular strands of total density v = v_E + v_X, where v_E is the entangled strand density inferred from melt elasticity measurements of uncrosslinked PS and v_X is the density of crosslinked strands determined from the ratio of the applied electron dose to the electron dose for gelation. when v is less than 4 × 10²⁵ m^?3 (<1.3v_E), only crazes are observed whose microstructure is similar to those in uncrosslinked PS. As v increases from 4 × 10²⁵ to 8 × 10²⁵ m^?3 (from 1.3v_E to 2.5v_E) shear deformation begins to compete with crazing. As v increases above 8 × 10²⁵ m^?3, only shear DZs are observed, the strain in which becomes progressively more diffuse as v increases. The λ in the crazes and DZs correlate well with λ_max, the maximum extension ratio of a strand in a network of density v computed using the Porod×Kratky model. For crazes ln(λ) ? 0.9 ln(λ_max) and for DZs ln(λ) ? 0.55 ln(λ_max). The strain at which crack nucleation is first observed increases as v increases from <5% in uncrosslinked PS with v = 3.3 × 10²⁵ m^?3 to >20% in PS with v = 33 × 10²⁵ m^?3 (v = 10v_E); crosslinking to still higher crosslink densities, e.g., v = 14v_E, results in cracks which propagate in a catastrophic manner at low applied strains. An optimum v thus exists, one not too high to suppress local shear ductility but high enough to suppress crazes which can act as crack nucleation sites. these results are compared with previous results on a variety of linear homopolymers, copolymers, and polymer blends that are characterized by a wide range of v (v = v_E). The transitions from crazing to crazing plus shear and from crazing plus shear to shear only take place at almost identical values of v. In addition the correlation between λ in the crazes and DZs and λ_max for a single network strand is the same for both classes of polymers. This agreement implies that chain scission is the major mechanism by which strands in the entanglement network are removed in forming fibril surfaces. Craze suppression, by either increasing v in the crosslinked polymer or v_E in the uncrosslinked ones, is due to the extra energy required to break more main-chain bonds to form these surfaces.     

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.     

Stress-optical behavior of cycloaliphatic polyesters

Stress-strain-birefringence measurements were carried out on elastomeric networks of poly(oxymethylene-1,4-cis-cyclohexylenemethyleneoxysebacoyl) at several temperatures between 5 and 80°C. The dependence of both the birefringence Δn and the true stress f/A on temperature was found to be linear for T > 30°C; for T < 30°C an anomalous increase in the birefringence and a sharp decrease in the stress was observed. This behavior suggests that crystallinity is developed in the strained networks at low temperatures, and the crystallites are oriented in the direction of the elongation. Values of the optical configuration parameter Δa ranged from 9.15 to 8.28 in units of 10²⁴ cm³ in the temperature range studied. The value at 40°C of 10²⁴Δa, obtained from experiments performed on swollen networks, amounted to 7.47 cm³. These results suggest that intermolecular interactions enhance the birefringence of the strained networks. The quantities Δa and d In Δa/dT were calculated by using the valence optical scheme. Although the calculations reproduce the temperature coefficient fairly well, the theoretical values of Δa are smaller than the experimental ones. The agreement between theory and experiment is better assuming that the CH₂CH₂? COOCH₂ segment is freely rotating.     

Deformation of polybutene-1 spherulites

The deformation of fresh and aged polybutene-1 spherulitic samples has been investigated by microscopic observation, interferometry, studying macroscopic and spherulitic birefringence changes, and study of light-scattering patterns. The spherulite deformation is not affine, the microscopic deformation ratio being less than the macroscopic deformation ratio of the sample and greater in the equatorial regions of the spherulite than in the polar regions. The deviation from affine deformation is less for fresh spherulites than for the aged, where void formation occurs in the equatorial part of the spherulite. This gives rise to large scattering by this part of the spherulite and to form birefringence. The spherulite birefringence and its change with elongation is dependent upon the degree of aging of the sample. The spherulite birefringence is more negative for the aged sample. In the polar regions of the spherulite, this negative birefringence decreases and turns positive at higher elongations, characteristic of a reorientation of the crystals with their optic axes turning from being perpendicular to parallel to the spherulite radius. The spherulite birefringence in the equatorial direction becomes somewhat more negative on stretching a fresh sample but less negative on stretching an aged one. Spherulite distortion and orientation changes are apparent from the light-scattering patterns of films possessing small spherulites. The changes in V_v and H_v scattering patterns upon stretch are different for the fresh and aged samples. The V_v patterns of the fresh samples decrease in intensity with time after stretching a fresh sample with the H_v patterns do not.     

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.     

“Experimentation and modeling for the apparent elongation viscosity of polymer melts with the White–Metzner model”

The measurement of the apparent elongation viscosity (η_e) of several polyolefin melts was conducted in this study by using the isothermal fiber‐spinning method. The White–Metzner (W–M) model was used to analyze the spinning flow of the polymer melts and, thus, the elongation viscosity was predicted at elongation strain rates ranging from 0 to approximately 5 s^?1. The values of the model parameters required in the W–M model were obtained by curve fitting the experimental data obtained from the shear measurements. The elongation viscosity predicted using the W–M model was in good agreement with the experimental results of fiber spinning. In addition, η_e could also be estimated directly from the measured shear viscosity (η_S) with a formulation using the W–M model; the subsequently obtained elongation viscosity and Trouton ratio (T_R) were reasonable within a wide range of strain rates. Based on the experimental and theoretical results, the polyolefin with a high molecular weight was observed to have high elongation viscosity, and the polymer with a broad molecular weight distribution also possessed high η_e. The T_R value of the commercial polypropylene (PP‐1040) began to increase from 3 at a deformation rate of 0.1 s^?1 and grew up asymptotically to 10, whereas the T_R of high‐density polyethylene (HDPE‐606) remained nearly at 3 within the entire range of strain rates. Copyright © 2014 John Wiley & Sons, Ltd.     

Molecular orientation of aromatic polycarbonates containing fluorene side chains by polarized infrared spectroscopy and birefringence analysis

The molecular orientation of an aromatic polycarbonate containing fluorene side chains was investigated by polarized infrared spectroscopy and birefringence analyses. The copolymers were synthesized from 2,2‐bis(4‐hydroxyphenyl)propane (BPA), 9,9‐bis(4‐hydroxy‐3‐methylpheny)fluorene (BMPF), and phosgene by interfacial polycondensation. The 1449‐cm^?1 band of the uniaxially oriented films, stretched at the glass‐transition temperature (T_g) plus 5 °C, was assigned to various combinations of CC stretching and CH in‐plane bending vibrations in the fluorene ring, and the transition moment angle was estimated to be 90°. The intrinsic birefringence of aromatic polycarbonate films with BMPF molar ratios ranging from 0.5 to 1 was obtained with the 1449‐cm^?1 band. The copolymer was estimated to show zero intrinsic birefringence at the BMPF molar ratio of 0.75, and the BMPF homopolymer showed negative intrinsic birefringence. A linear relationship between the volume fraction of BMPF units and the intrinsic birefringence indicated that the two monomer units of BPA and BMPF in each copolymer were not independent, and an intrinsic birefringence could be defined even in the copolymer. The sign of the photoelastic coefficient in the homopolymer with BMPF units was positive. The different signs of the photoelastic coefficient and the intrinsic birefringence suggest that the fluorene side‐chain orientation induced by stress in the glass state is quite different from the orientation of the uniaxially oriented films stretched at T_g + 5 °C. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1554–1562, 2003     

Uniaxial Draw Of Poly(aryl-ether-ether-ketone) by solid-state extrusion

Poly(aryl-ether-ether-ketone) (PEEK) films and rods have been solid-state extruded at 154 and 310°C, respectively. The crystal orientation functions, melting behavior, density, and tensile properties of the drawn PEEK films (EDR ≤ 3.7) and rods (EDR ≤ 5.5) have been measured. As extrusion draw ratio (EDR) was increased, the c-axis orientation function, melting temperature, and tensile modulus and strength increased. Moduli up to 6.5 GPa and the strengths up to 600 MPa, 3 and 6 times the values of undrawn films, respectively, were obtained for the drawn films. The thermal expansivities along (α_‖) and perpendicular (α_?) to the draw direction of PEEK rods were measured from ?40 to +10°C. As EDR was increased, α_? increased, but α_‖ decreased. At EDRs of 3.8 and 5.5, α_‖ even exhibited negative values (about ?5 × 10^?6°C^?1), probably due to reversible contraction of elongated tie-molecules.     

Molecular orientation induced by cooling stresses. Birefringence in polycarbonate: III. Constrained quench and injection molding

Residual stress and birefringence distributions are determined in polycarbonate samples obtained by quenching in a specially designed apparatus and by injection molding. The molecular orientation is distinguished from the thermally and pressure-induced residual stresses. The birefringence in the quenched samples is found to be positive and almost constant, independent of the quench temperature, but varying strongly with initial quench temperature between 150 and 180°C. The residual stress level, as determined by layer removal and sectioning, is very low. The birefringence distribution is mainly due to a tensile equibiaxial orientation induced by transient cooling stresses built up above T_g. The samples which are injection-molded with a high injection speed and without packing pressure display the same birefringence distribution as the quenched samples, apart from a local maximum beneath the surface due to the shear flow during filling. Apart from the flow during filling and packing, the frozen-in molecular orientation in injection-molded samples is also induced by transient thermal stresses present during vitrification. The birefringence from thermally induced orientation was found to be of comparable magnitude to that from flow-induced orientation. For a correct prediction of molecular orientation the thermal strains above T_g must therefore be included in simulation programs. Because of the low level of thermal stresses, the application of a packing pressure will lead to tensile stresses at the surface in general. © 1994 John Wiley & Sons, Inc.     

Étude des spectres infrarouges de divers dialcoyl-diméthoxy-stannanes

The infrared absorption spectra of some dialkyldimethoxystannanes have been investigated in the 400–1500 cm^?1 region. The bands associated with v_s(SnC₂) and v_s(SnO₂) vibrations have been found at 510–521 cm^?1 and 466–475 cm^?1. The group of bands between 560 and 620 cm^?1 is assigned jointly to v_a(SnC₂) and v_a(SnO₂) vibrations. v(C? O) of the methoxy groups linked to tin appears at 1064–1068 cm^?1.     

Experimental study of the D + H2 (v = 1) reaction by CARS spectroscopy

The reactions D + H₂ (v = 0, 1) → HD (v = 0, 1) + H have been studiedin a discharge flow reactor by CARS-spectroscopy. For H₂(v = 0) molecules a rate constant of (4, 0 ± 1, 0) 10^?16 cm³ s^?1 is obtained at 310 K from measured HD (v = 0, 1) product yields. Keeping the degree of vibrational excitation of H₂in the microwave discharge in the range of 1% from the increase of the HD (v = 0, 1) CARS signals a rate of k_{2a, b} = (1, 0 ± 0, 4) 10^?13cm³ s^?1 is derived. The total consumption of H₂ (v = 1) in the presence of D atoms gives a rate k₂ = (1, 9 ± 0, 2) 10^?13 cm³ s^?1 at 310 K. The resultsare discussed in regard to previous measurements and theoretical treatments.     

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.