Stress-optical Coefficient Research Articles

Microstructural Dynamics of a Homopolymer Melt Investigated Using Two-Dimensional Raman Scattering

The microstructural dynamics of polyisobutylene have been investigated using a new rheooptical technique, two-dimensional Raman scattering (2D Raman). 2D Raman employs intrinsic bond vibrations to selectively resolve the segmental dynamics within a material subjected to small-amplitude oscillatory deformation. In addition, interspecies interactions are probed through a cross-correlation of the orientation-induced response from distinct Raman peaks. It has been observed that the motions of the main chain and side groups in polyisobutylene are affected independently as the mechanical frequency is increased from the rubbery plateau into the glassy regime. In particular, at low frequencies ( 10 s -1 ), the groups reorient independently as the mechanical glass transition is approached. The results are in accord with the observed frequency dependence of the stress-optical coefficient.

鉛ガラスから製造した光ファイバのファラデー効果を利用した電流センサ

For application to current monitoring in electric power facilities, the authors have been developing a current sensor utilizing the Faraday effect of an optical fiber manufactured from flint glass having a very small stress-optic coefficient. This paper describes the result of study on constructing the sensing system, which is composed of a sensor head, a light source, fibers for light transmission and a signal processing circuit. First, results from investigation are reported with respect to causes affecting performance and durability of the sensor, and examinations of countermeasures also are described. As a result of the research, it was confirmed experimentally that several means are effective to improve characteristics of the sensor. Then, design and test results of a sensor model constructed with application of the means are described. From the test results it was proved that the model shows excellent characteristics satisfying basic requirements of the standard for conventional current transformers. © 1997 Scripta Technica, Inc. Electr Eng Jpn, 118 (3): 22–38, 1997

Limitation of Stress-Optical Rule for Polymeric Liquids

In this note, we deduce from existing experimental data for real polymers that the stress-optical rule is valid only approximately and may not be valid even approximately for polymers with low stress-optical coefficients

Dynamic Birefringence of Amorphous Polyolefins II. Measurements on Polymers Containing Five-Membered Ring in Main Chain

Five amorphous polymers are synthesized from five membered cyclic olefins to examine the strain-induced birefringence and viscoelasticity. The complex Young’s modulus and the complex strain-optical ratio are measured from the rubbery plateau to the glassy zones of viscoelasticity. The stress-optical coefficients in the rubbery plateau zone, CR, of the five polyolefins are all positive and very close to each other. This result means that the value of CR is relatively insensitive to the details of molecular structure for this kind of polyolefins. The stress-optical coefficients in the glassy zone, CG, of the four polyolefins which do not contain benzene rings are all negative and small numbers if compared with those of polymers with the benzene rings.

The reptation model with segmental stretch

Numerical predictions of the Doi-Edwards tube model with segmental stretch and a freely jointed chain spring model are presented for steady two-dimensional flows with a continuously varying degree of extensional and shear character. Our results are obtained from three sets of calculations by considering the effect of the flow-type parameter, the molecular weight and the number of entanglements per chain on the model predictions. The predicted degree of stretch and orientation, as well as specific rheological and optical properties that can be measured experimentally are presented. As anticipated, calculations reveal that the 'orientational' dynamics are controlled by the reptative tube disengagement process, whereas the stretching process is controlled by the Rouse dynamics. Inclusion of segmental stretch fundamentally alters the character of the Doi-Edwards model. Calculations reveal that as the flow becomes increasingly extensional in character, significant steady state stretch is predicted with a commensurate modification of the material functions. According to calculated results, it is possible to have significant chain stretching without producing measurable changes in the stress optical coefficient.

Rheo-optical investigation of a polystyrene melt

The transient birefringence and the transient tensile stress of a polystyrene melt at 140°C elongated with constant stretch rate and constant Hencky strain rate (ϵ) are presented. Compared with the response during linear viscoelastic deformation, the values of the reduced birefringence and the reduced stress are higher when the elongation is performed with ϵ = const., and are lower when the elongation is carried out with λ = const., The stress-optical coefficient turns out to be a function of duration and rate of deformation.

Sub-Tg relaxation in Ge5Se95 and As5Se95 glasses

Abstract High-purity Ge 5 Se 95 (glass transition temperature, T g = 75°C) and As 5 Se 95 ( T g = 52°C) bulk glasses were prepared by melting pre-distilled or surface oxide-removed 5 and 6N pure raw materials in a fused silica ampoule. The density, ϱ, shear modulus, G , Poisson's ratio, ν, heat capacity, C p , and stress-optic coefficient, B , at λ = 1.8 μ m were measured periodically over about 7 months after cooling to room temperature. In between the measurements, glasses were stored stress-free at room temperature (∼ 20°C) in darkness. For both glasses, the magnitude of B increased by about 50% in a near-exponential manner over the initial 14-day period and leveled thereafter. Associated with the relaxation of B , there appeared some increased, although no more than one standard deviation from the average, in the density and elastic properties of Ge 5 Se 95 . The elastic properties of As 5 Se 95 appeared relatively constant over the 14-day period. The shape of the C p versus T curves for both the glasses changed in the transition region. The relaxation resulted in an increase in the glass transition temperature (defined by the onset of the endothermic transition), with a concurrent decrease in the fictive temperature (defined by the equivalent enthalpy). It is suggested that the Ge(As) atoms are under-coordinated in the initial structure, and that the sub- T g structural relaxation involves coordination changes of these atoms effective increased degree of crosslinking with time.

Dynamic birefringence of amorphous polymers

The studies on dynamic birefringence of amorphous polymers are reviewed. The birefringence in oscillatory deformation is related to the viscoelasticity through the stress-optical rule (SOR) in the rubbery and the terminal flow zones. The deviation from the SOR in the glassy and the glass-to-rubber transition zones can be described with a modified SOR, based on the assumption that the stress is a sum of two components associated with respective stress-optical coefficients. Experimental results are reviewed for 14 polymers: polystyrene, poly(α-methyl styrene), poly(2-vinyl naphthalene), polyisobutylene and 10 polymers for engineering plastics. The nature of various parameters is discussed in relation to the molecular structure.

Life-time renormalization in critical dynamics as applied to the isotropic-nematic transition in sidechain liquid crystalline polymers

We study the dynamic behavior near the isotropic-nematic transition in liquid crystalline sidechain polymers using a mode coupling technique as applied to the life-time renormalization. To lowest order in mode coupling we find for the dynamical critical exponent z for the relaxation time of the order parameter the value z = 1.5 while in mean field approximation one obtains z = 1. This result is in agreement with recent experiments done in Martinoty's group on two different classes of sidechain liquid crystalline polymers using electric and acoustic birefringence measurements. This qualitative difference in behaviour between low molecular weight systems and sidechain polymers can be traced back to nonlinear (cubic) cross coupling terms in the generalized energy between the order parameter and the strain associated with the transient network. The importance of such nonlinear cross coupling terms is corroborated further by recent measurements of the dynamic stress-optical coefficient in sidechain elastomers.

Diffusion, rheology, and flow birefringence in block copolymer liquids near the ordering transition

AbstractMeasurements of the diffusion and relaxation of block copolymer chains near the order‐disorder transition (ODT) are reported. Forced Rayleigh scattering has been used to determine the diffusivities parallel and perpendicular to the lamellar planes, for poly(ethylene‐propylene)‐poly(ethylethylene) (PEP‐PEE) melts. The anisotropy is relatively weak (i.e., less than a factor of 4), but increases steadily as temperature is decreased. Rheology and flow birefringence have been employed to examine the conformational dynamics in block copolymer solutions. For PEP‐PEE in squalane, the stress‐optic relation is approximately valid, but the stress‐optic coefficient increases in the ordered state. The location of the ODT is consistent with the dilution approximation. For polystyrene‐polyisoprene (PS‐PI) diblock and triblock copolymers, the stress‐optic relation fails completely. There is evidence that the fluctuation regime (i.e., in the disordered state but near the ODT) may be considerably broader in block copolymer solutions than in melts. Furthermore, the onset of structure in the solution is accompanied by substantial form birefringence. In general, the optical signals are more complicated than the Theological ones, but also much more sensitive to small changes in temperature or concentration.

Dynamic Birefringence of Amorphous Polyolefins I. Measurements on Poly[1-ethyl-5-methyl-octahydro-4,7-methano-1H-indene-12,3-diyl

The complex strain-optical coefficient and the complex Young’s modulus of an amorphous polyolefin, poly[1-ethyl-5-methyl-octahydro-4,7-methano-1H-indene-12,3-diyl], PEMOMID, were measured around the glass-to-rubber transition zone. The data was analyzed with a modified stress-optical rule, and two components of complex modulus, EG* and ER*, and two associated stress-optical coefficients, CG and CR, were determined. The result was compared with one for a Bisphenol A polycarbonate, PC. CR, stress-optical coefficient in the rubbery plateau zone, for the polyolefin was 1.7×10−9 Pa−1 and about three times smaller than that for PC. CG for PEMOMID is negative and this was in contrast to a usual positive value for polymers containing phenyl rings in their repeating units.

Stress-optic coefficient of GeAsSe chalcogenide glasses

Abstract Stress-induced optical retardation at λ = 1.8 μm in GeAsSe chalcogenide glass disks subjected to a diametral compressive load was measured using a modified IR-polarizing microscope. The computed stress-optic coefficient, B, varied from −29.6 to +5.4 TPa−1 over the glass-forming region. Although the magnitude of B appeared to decrease with increasing Ge content, there appeared to be little direct correlation between B and the average coordination number, 〈(ifr)〉.

高分子材料 ＰＳ／ＰＣブレンドと共重合体の粘弾性と複屈折

The complex Young's modulus, E*(ω), and the complex strain-optical coefficient, O*(ω), of a polystyrene (PS)/bisphenol A polycarbonate (PC) blend and a graft copolymer were studied in the glass-to-rubber transition zone at frequencies ranging from 1 to 130Hz at various temperatures between 102°C and 182°C. The relaxation behaviors in E*(ω) and O*(ω) of two alloys were compared with each other in relation to the relaxation behaviors of constituents, PS and PC. It was clarified that for the blend in the mechanical spectrum two isolated relaxation peaks are detected at frequencies apart from each other, which means that the consitituents relax independently. For the copolymer two relaxation peaks of constituents were almost merged giving rise to about a single peak which indicates cooperating relaxation of the two components.The optical relaxation spectra, O*(ω), of two alloys showed distinct difference in quality and it also made us predict their compatibility to some extent. For both alloys, the stress-optical coefficient, CR, in the rubbery zone was reduced to 1/4-1/6 of the absolute value of components polymer as a result of compensation of the opposite-signed birefringences of constituent polymers. The photoelastic coefficient, Cd, for two alloys and the component polymers, PS and PC, exhibited a strong correlation with the stress-optical coefficient, CR.

Mode coupling theory of the isotropic-nematic transition in sidechain liquid crystalline polymers

Using a mode coupling technique we investigate the dynamics near the isotropic-nematic transition in liquid crystalline sidechain polymers. While in mean field approximation one obtains z = 1 for the dynamical critical exponent z for the relaxation time of the order parameter, we get from mode coupling the value z = 1.5, a result which is in agreement with recent experiments done in Martinoty's group on two different classes of sidechain liquid crystalline polymers using electric and acoustic birefringence measurements. An analysis of recent measurements of the dynamic stress-optical coefficient in sidechain elastomers shows that mode coupling effects are also important in that case.

A brief review of photo-orthotropic elasticity theories

The development of the theory of birefringence of annotropic composites has proceeded mainly along the following directions, strew strain models, analogy, integrated photoelasticity and tensonal nature of birefringence. All these studies have concluded that three independent photoelastic constants are needed to characterize orthotropic model materials. In the literature, there has not been uniformity of notation used in the representations of the results.In this paper, using uniform notation, existing photo-orthotropic clasticity theories are reviewed under three major headings stress-optic laws strain-optic laws and approximate strain-optic laws. The interrelation ships between stress-optic and strain-optic coefficients are brought out Interpretation of isoclinics is discussed. The steps necessary to calibrate a birefringent orthotropic composite are summarized and finally the influence of residual birefringence is also discussed.

Near-critical behavior of the dynamic stress-optical coefficient in liquid crystalline elastomers

Dynamic stress-optical measurements on liquid crystalline elastomers with different crosslinking densities have been carried out in the isotropic phase. The appearance of two relaxation processes in the spectra is probably due to the side-on attachment of the spacers to the mesogenic groups. The relaxation frequencies and the relaxation strength of the processes show critical behavior in qualitative agreement with the Landau-de Gennes theory. The strong cross-linking density dependence of the relaxation strengths provides evidence that the cross-linking points locally perturb the liquid crystalline order

Viscoelasticity and birefringence of bisphenol A polycarbonate

The dynamic Young's modulus, E *, and birefringence of bisphenol A polycarbonate were measured over the glassy to rubbery plateau zone. Measurements were performed over the frequency range of 1 to 130 Hz at various temperatures between 148 and 170°C. A modified stress-optical rule was applied in characteristic analysis of the glassy and glass transition regions. It was earlier proposed to replace the stress-optical rule which, generally, was valid only at relatively low frequencies corresponding to rubbery plateau and rubbery flow regions. E * could be separated into two component functions, E * R and E * R. The stress-optical coefficients, C R and C G, associated with the respective components were 5.0 × 10 −9 and 3.5 × 10 −11 Pa −1. In constructing master curves of E * R and E * G with the method of reduced variables, an unlike temperature dependence was found. This result could account for the breakdown of the time-temperature superposition principle for E * reported by several investigators.

The dispersion of birefringence in photoelastic materials

AbstractA spectral analyser was used to determine the variation with wavelength known as the dispersion of birefringence of the fringe constant f and the stress optic coefficient C for photoelastic materials. A disc was loaded diametrically and was subjected to the stress freezing thermal cycle. The intensity was measured along the diameter perpendicular to the load for wavelengths between 450 and 850 nm at 5 nm intervals. Using the theoretical solution to the stresses it was possible to calculate the stress optic coefficient for all wavelengths employed. A similar technique was used for an identical disc that was loaded at room temperature.It was found that the fringe constant was extremely linear with wavelength for both types of loading and for the materials CT200, CT1200 and MY750. The stress optic coefficient did not change much between sheets of the same material but was markedly different between materials. The dispersion of birefringence was found to be approximately constant but showed evidence of anomalous dispersion.

Stress-strain relations and molecular orientation in highly crosslinked cis-polyisoprene networks

Results of equilibrium stress-strain experiments and Fourier transform infra-red measurements of segmental orientation, previously reported for moderately crosslinked cis-polyisoprene networks by Amram et al. ( Polymer 1986, 27, 877), are extended to networks with high degrees of crosslinking. The samples were stretched to the limit of maximum chain extensibility. The absence of strain-induced crystallization during experiments was inferred from infra-red measurements, according to which the 844 cm −1 absorption band specific to crystalline regions did not exhibit any systematic shift in one direction. The reduced force versus inverse extension ratio showed strong upturns while the reduced orientation curves did not exhibit any upturns. Likewise, the analogue of the stress optical coefficient, defined as the ratio of molecular orientation to true stress, exhibited a strong decrease with extension, in contrast to Gaussian networks in which it is approximately independent of the degree of deformation.

Digital birefringence measurement using the cross-correlation method

A digital system for measuring a small amount of birefringence or small changes in existing birefringences is presented. The apparatus is based on a data-acquisition system for a spectral-contents analysis. The use of cross-correlation techniques significantly reduces the data-processing time and permits measurement of the dispersion of the stress-optical coefficient of materials. The accuracy is of the same order as in the modulation techniques. The sensitivity of this method could be changed by changing the order of interference. A comparison is made with other existing polarization methods.