Mechanism of generation of photoelastic birefringence in methacrylate polymers for optical devices

We clarified the birefringence properties of poly(methyl methacrylate), poly(ethyl methacrylate), poly(isobutyl methacrylate), poly(cyclohexyl methacrylate), poly(isopropyl methacrylate), and poly(tert‐butyl methacrylate). We demonstrated that the conformational change in polymer molecules that causes orientational birefringence differs from that causing photoelastic birefringence. Orientational birefringence depends mainly on the orientation of the main chains of the methacrylate polymers above T_g. On the other hand, photoelastic birefringence in elastic deformation below T_g depends mainly on the orientation of the side chains while the main chains are scarcely oriented. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 2029–2037, 2010     

Anisotropic properties of poly(ethylene terephthalate) by Brillouin spectroscopy: Anisotropic properties of oriented bulk and nanostructured poly(ethylene terephthalate) determined by Brillouin spectroscopy and birefringence experiments

Using Brillouin spectroscopy (BS), the tensor of the elastic constants of oriented poly(ethylene terephthalate) was determined for a variety of morphologies obtained by different uniaxial drawing procedures. The extreme values of the moduli along the drawing direction at frequencies of a few gigahertz were C₃₃ = 40 GPa and C₄₄ = 1.8 GPa. As a result of the invariants of the single‐phase aggregate model, the oriented state is dominated by the Reuss average even at extreme draw ratios and subsequent to a deformation‐induced crystallization. This is documented in both the BS orientation parameter and the BS mode numbers in comparison with birefringence. Additional spectral lines observed at draw ratios larger than 6 are discussed in relation to the formation of nanostructured phases. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1201–1213, 2002     

Studies of the effect of orientation on the elastic constants of stretched and hydrostatically extruded polychlorotriflouroethylene: A reorientational model in semicrystalline polymers

A reorientational model of polymer solids is given. The solid is described as a collection of small, orientable units. The elastic constants of the oriented polymer are given as a combination of the elastic constants of the orientable units and of the orientation parameters 〈P₂(cosθ)〉 and 〈P₄(cosθ)〉. The elastic constants of stretched and hydrostatically extruded samples of polychlorotriflouroethylene are obtained with Brillouin light scattering. These are fitted to the model and the orientation parameters are calculated. The elastic constants from the extruded samples are fit well by the model but the fit to the stretched film is less satisfactory. Hydrostatic extrusion in polymers is thus assumed to be a reorientation process in the amorphous phase, but the stretching process is not completely reorientational.     

Assessment of thermal expansion coefficient of methylsilsesquioxane thin film

For the methylsilsesquioxane film whose optical birefringence is almost zero, it was recently reported that its vertical thermal expansion coefficient (CTE) was approximately one order of magnitude larger than the lateral CTE. Though the birefringence is not an absolute predictor of anisotropic behavior, the discrepancy in both the CTEs was so remarkable that it was essential to investigate whether the anisotropy was intrinsic property or not. If the effect of Poisson's ratio is considered in the calculation of the vertical CTE and when elastic modulus measured by surface acoustic wave spectroscopy is used in the assessment of the lateral CTE, both the CTEs are coincident with each other. Therefore, it can be concluded that the discrepancy in the CTEs can be attributed to a higher in‐plane polymer chain orientation but it can also arise from the misleadingly assumed modulus and Poisson's ratio. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3109–3120, 2006     

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     

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.     

On the refractive indexes and birefringence of nylon 6 yarns as a function of draw ratio and strain

A systematic study of the dispersion curves of the refractive indexes of nylon 6 yarns was made. The parameters were the draw ratio and strain. The measurements show that the dispersions of the refractive indexes n_∥ and n_⊥, parallel and perpendicular to the fiber axis, are equal, independently of draw ratio and strain. The average dispersion equals n_F ? n_C = 109 × 10^?4. Consequently, the birefringence is, within experimental accuracy, independent of the wavelength. The refractive indexes and the birefringence show a change in trend at 10–12% strain. This point corresponds to the yield strain in the stress–strain diagrams. The inference is that beyond the yield point the overall molecular orientation must increase less strongly with strain than before. An analysis shows that the Lorentz–Lorenz relation holds for the average refractive index n? = ? (n_∥ + 2n_⊥). So the change in n? versus draw ratio is mainly due to the change in density. By applying the Lorentz–Lorenz relation to the change of n? on straining, a value of Poisson's ratio (μ) could be derived. The average value found for nylon 6 yarns was μ = 0.48, which means that the density hardly changes with strain.     

Studies of molecular relaxation of poly(propylene oxide) solutions by dielectric relaxation and brillouin scattering

Dielectric relaxation and Brillouin scattering are jointly used in studying molecular relaxation in poly(propylene oxide) (PPO) and its solutions in methylcyclohexane. The dielectric method was applied to the more concentrated (100%, 80%, 60%, by volume) solutions over a wide temperature and frequency range (30 Hz to 8 GHz) in order that the variation in activation energy characteristic of a glass-forming substance could be delineated. The present work extends previous work on the undiluted polymer to higher frequencies so that range of 12 decades in the dielectric loss maximum f_max as a function of temperature is now available. The “Antoine” equation is found to represent the behavior of log f_max, of the bulk concentrated solutions very well. The more dilute (40%, 20%) solutions were studied only in the high-frequency (GHz) region since phase separation occurred at low temperatures. Both the temperature and dilution effects were interpreted in terms of free-volume theory. Brillouin scattering spectra were obtained at several scattering angles and a wide range of temperatures. A maximum in the curve of hypersonic attenuation versus temperature was observed in each polymer solution. The attenuation maximum shifts toward lower temperature upon dilution, in agreement with the dielectric relaxation result. The Brillouin scattering follows different activation parameters and evidences a more rapid process than does the dielectric relaxation. It is speculated that it monitors a secondary or subglass relaxation, due perhaps, to damped torsional oscillations.     

Structural analysis of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) fibers prepared by drawing and annealing processes

Structure of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) fibers prepared by drawing and annealing processes has been analyzed through wide-angle X-ray diffraction (WAXD), density, infrared dichroism, and birefringence measurements. There are three different types of crystalline structure in these fibers: two of these are the two types of orthorhombic with different orientation modes (the ordinary c-axis orientation (c//Z), and the preferential orientation of c-axis to the direction perpendicular to the fiber axis (c⟂Z)); and the third is pseudohexagonal. The weight fractions of the three types of crystals and amorphous phase were analyzed combining the WAXD integrated intensity and density data. The relation between crystalline orientation factors obtained separately from the WAXD measurement and the infrared dichroic ratio is also discussed. The birefringence of these fibers shows negative and positive values, depending on drawing and annealing temperatures. Considering the intrinsic birefringence and weight fraction of the c//Z, c⟂Z, and pseudohexagonal crystals, birefringence of the amorphous phase was evaluated. The amorphous birefringence shows positive values and decreases with an increase in the annealing temperature. From the analyzed fiber structure, it was speculated that the c⟂Z and pseudohexagonal crystals are preferentially formed in the drawing process irrespective of the drawing temperature.© 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2471–2482, 1998     

Simultaneous determination of elastic and optical properties of polymers by high performance Brillouin spectroscopy using different scattering geometries

General aspects of high performance Brillouin spectroscopy in polymers using special scattering geometries such as 90A-scattenng geometry are discussed. Technical improvements are reported resulting in absolute accuracies up to 0.05 % for sound velocity determination. A method of data analysis is presented delivering simultaneously the complete set of elastic stiffness constants. The influence of birefringence on the Brillouin line shifts in anisotropic polymeric systems is estimated and techniques to reduce this influence are proposed. The determination of the principal refractive indices by Brillouin spectroscopy is discussed. Furthermore, a quantityD ^X , which is sensitive to hypersonic relaxation processes, is introduced.Dedicated to Prof. Dr. H.-G. Kilian on the occasion of his 60th birthday.     

Miscibility and orientation behavior of poly(vinyl alcohol) / poly(vinyl pyrrolidone) blends

The miscibility of poly(viny1 alcohol)/poly(vinyl pyrrolidone) (PVA/PVP) blends is investigated by differential scanning calorimetry (DSC) and wide-angle x-ray diffraction (WAXD). The molecular orientation induced by uniaxial stretching of the blends is also examined by WAXD and birefringence measurements. It is shown by the DSC thermal analysis that the polymer pair is miscible, since a single glass transition temperature (T_g) is situated between the T_gs of the two homopolymers at every composition. The T_g versus composition curve does not follow a monotonic function but exhibits a cusp point at a PVP volume fraction of a little under 0.7, as in a case predicted by Kovacs' theory. The presence of a specific intermolecular interaction between the two polymers is suggested by an observed systematic depression in the melting point of the PVA component. A negative value of the polymer-polymer interaction parameter, χ₁₂ = 0.35 (at 513 K), is estimated from a thermodynamic approach via a control experiment using samples crystallized isothermally at various temperatures. The extent of optical birefringence (Δn) of the drawn blends decreases drastically with increasing PVP content up to 80 wt %, when compared at a given draw ratio, and ultimately Δn is found to change from positive to negative at a critical PVP concentration of a little over 80 wt %. Discussion of the molecular orientation behavior takes into consideration a birefringence compensation effect in the miscible amorphous phase due to positive and negative contributions of oriented PVA and PVP, respectively.     

Mechanical properties of the novel organometallic polymer poly(ferrocenyldimethylsilane)

A study of the mechanical properties of poly(ferrocenyldimethylsilane) [Fe(η‐C₅H₄)₂SiMe₂]_n, 3 , a novel organometallic polymer, has been performed on thin films of this material. The Young's modulus and Poisson's ratio of film samples (15 × 1 × 1 mm) of 3 were measured in quasi‐static tension using a video extensometer. For 3 , the values of the Young's moduli (E) and Poisson's ratios (ν) were similar between axes in the plane and independent of the splicing direction used during sample preparation. The mean and standard deviation of the Young's modulus and Poisson's ratio were 0.78 ± 0.08 GPa and 0.37 ± 0.06 GPa, respectively. Thermomechanical analysis of 3 revealed a steady decrease of E from a room temperature value of approximately 0.70 GPa. Additionally, it was found that at 150 °C, 3 was unable to support even small stresses, consistent with the onset of a melt transition (ca. 135 °C). A mathematical model based on molecular geometry is developed to describe the results. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2280–2288, 2005     

Brillouin scattering of oriented films of poly(vinylidene fluoride) and poly(vinylidene fluoride) -poly( methyl methacrylate) blends

Temperature dependent Brillouin scattering studies of PVF₂ films stretched to various stretch ratios have been carried out. Elastic constants for unstretched and stretched films have been obtained as functions of temperature. The elastic constant C₃₃ of the stretched films has a greater temperature dependence than that of unstretched films. To elucidate the effect of the surrounding amorphous matrix on the Brillouin spectrum of semicrystalline PVF₂ film, we carried out Brillouin scattering studies of films made from blends of PVF₂ and PMMA.     

Theoretical prediction of the structural,elastic, electronic,optical and thermal properties of the cubic perovskites CsXF3 (X = Ca,Sr and Hg) under pressure effect

Some physical properties of the cubic perovskites CsXF₃ (X = Ca, Sr and Hg) have been investigated using pseudopotential plane-wave method based on the density functional theory. The calculated lattice parameters within GGA and LDA agree reasonably with the available experimental data. The elastic constants and their pressure derivatives are predicted using the static finite strain technique. We derived the bulk and shear moduli, Young's modulus, Poisson's ratio and Lamé’s constants for ideal polycrystalline aggregates. The analysis of B/G ratio indicates that CsXF₃ (X = Ca, Sr and Hg) are ductile materials. The thermal effect on the volume, bulk modulus, heat capacity and Debye temperature was predicted.     

Optical,mechanical, and photoelastic anisotropy of biaxially stretched polyethylene terephthalate films studied using transmission ellipsometer equipped with strain camera and stress gauge

The anisotropic properties of polyethylene terephthalate film resulting from its manufacturing process are quantitatively investigated in terms of its optical, mechanical, and photoelastic aspects. Transmission ellipsometers and a Jones‐matrix‐based analysis software together with a 4 × 4 Berreman‐matrix‐based analysis software are adopted to determine the wavelength‐dependent in‐plane birefringence, the principal refractive indices, and the orientation of the optical axis. Mechanical anisotropy is characterized in terms of the elastic compliance tensor components using the measured azimuthal angle‐dependent Young's modulus and Poisson's ratio. From the measured variation of the wavelength‐dependent in‐plane birefringence as a function of tensile stress, the dispersive photoelastic coefficients are obtained for a few sample azimuthal angles, and the components of the photoelastic tensor are determined. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 152–160     

Rayleigh-brillouin spectroscopy of syndiotactic poly(n-butyl methacrylate) near the glass transition

We present Rayleigh-Brillouin light scattering data of highly syndiotactic poly(n-butyl methacrylate) [PBMA] whose glass transition temperature as measured by DSC is 55°C. The Brillouin peak shifts, Brillouin peak widths, and Landau-Placzek ratios from ?15 to 130°C are reported. The Brillouin peak widths decrease continuously through the glass transition region. This indicates a continual decrease in the strength of processes whose relaxation times are about 10^?10 s with decreasing temperature even as the system becomes glassy. The Landau-Placzek ratio above the glass transition is about 3, indicating the high optical purity of our sample. This low Landau-Placzek ratio arises from the sample's homogeneous stereochemistry. Some of the anomalous behavior observed around 40–50°C in previous PBMA studies is explained in terms of syndiotactic regions within a largely atactic sample.     

Quantitative characterization of deformation in drawn polypropylene films

The submicroscopic morphology of uniaxially deformed isotactic polypropylene films has been examined by small-angle light scattering (SALS), electron microscopy, optical microscopy, small-angle x-ray scattering (SAXS), wide-angle x-ray diffraction, birefringence, sonic modulus, and density methods. Several new interpretations and extensions of existing theories are developed and verified experimentally as follows. (1) The V_v SALS pattern is shown to be a new tool for the identification of the sign of the birefringence of spherulites too small to be seen in the optical microscope. The theoretical dependence of the V_v SALS pattern is developed and verified experimentally with patterns from isotactic polypropylene, polyethylene, Penton, nylon 6,6, poly(ethylene terephthalate), and nylon 6,10. (2) Intraspherulitic lamellar behavior during deformation can be identified from the SAXS pattern. This includes quantitative evaluation of the long spacing between lamellae and their average orientation. (3) The two-phase sonic modulus theory is valid over the wide range of deformations, crystallinities, processing temperatures, and molecular weights used in this study. The deformation of isotactic polypropylene films drawn at 110 and 135°C. has been characterized quantitatively in terms of an integrated picture of mass movement on all morphological levels: the molecular, the interlamellar, and the spherulitic. At both temperatures, the spherulites deform affinely with extension, whereas the deformation mechanisms within the spherulite depend on the location of the radii with respect to the applied load. During spherulite deformation, lamellar orientation and separation processes predominate, whereas at high extensions, fibrillation occurs and crystal cleavage processes predominate. The noncrystalline region orients throughout the draw region. At 135°C. non-orienting relaxation processes appear in the noncrystalline region which retard the rate of molecular orientation with extension.     

The orientational state of uniaxially stretched PMMA

Uniaxially stretched samples of PMMA were investigated by Brillouin Spectroscopy (BS). From the velocity of hypersound we could determine most of the elastic constants. Using a recently developed analysis [1] it is demonstrated that the properties of this polymer can be well described by the aggregate model. This result offers the possibility of mapping the mechanical properties by birefringence measurements. The dependence of the fourth momentP ₄ on the second momentP ₂ is identical with that determined for PC [2] and follows, in the measured range, that of an affine orientational state. Nevertheless, the dependence on the stretching ratio differs for different molecular weights. Thus the partition of the deformation into an orientational and an elongational contribution, as has been proposed [3], seems to be well founded.The partition depends on the stretching conditions.     

Ultrasonic and hypersonic dispersion in polysiloxanes

We report ultrasonic attenuation and velocity measurements on poly(dimethylsiloxane) (PDMS), poly(phenylmethyl siloxane) (PPMS), and copolymer poly(dimethyl phenylmethyl siloxane) in the temperature range of 10–50°C and frequency 0.3–45 MHz. The present data complement previously reported Brillouin spectra at hypersonic frequencies. Whereas the ultrasonic velocity u₀ is virtually independent of frequency, the ultrasonic absorption exhibits strong dispersion which can be ascribed to the viscoelastic normal mode relaxation. The ultrasonic attenuation data for PPMS at low temperatures display an additional relaxation process related to localized segmental motion. This mode is also responsible for the relatively large dispersion of the sound velocity and attenuation in the gigahertz frequency range accessible to the Brillouin scattering experiment. The extended information, which can be extracted by studying hypersonic dispersion, is discussed in detail.     

The mechanical moduli of lamellar semicrystalline polymers

Bounds on the elastic constants are derived for semicrystalline polymers whose local morphology is lamellar. Local response matrices (stiffness and compliance) are formulated in three dimensions that simultaneously incorporate uniform in-plane strain and additive forces from layer to layer of crystalline and amorphous phases and uniform stress and additive displacements normal to the lamellar surfaces. Spatial averaging of the stiffness and compliance matrices under the assumption of axially symmetric orientation gives the upper and lower bounds on the longitudinal and transverse tensile moduli and the axial and transverse shear moduli as functions of the separate phase elastic constants, the volume percent crystallinity, and the moments of the orientation 〈cos²θ〉 and 〈cos⁴θ〉. The bounds are much tighter than the Voight upper and Reuss lower bounds that do not recognize phase geometry. Using the known crystal elastic constants of polyethylene, sample calculations on isotropic unoriented materials show that the divergence of bounds at high crystallinity necessitated by the extreme crystal anisotropy shows up only at very high crystallinity. At low temperature the bounds are tight enough to specify G₁, the amorphous modulus, from the measured G and the known crystal elastic constants. At higher temperatures and lower G, the bounds are not tight enough for this purpose but the shear modulus versus crystallinity and temperature data are well fitted by the lamellar lower bound using a temperature-dependent, crystallinity-independent G₁.