General description of mechanical anisotropy of semicrystalline polymers in relation to orientation of structural units composed of crystalline and noncrystalline materials

A mathematical representation of the transformation of an orientation function between two sets of Cartesian coordinates is discussed in terms of a series expansion of the distribution function in generalized spherical harmonics. A general procedure for calculating the mechanical anisotropy of a single-phase system (a polycrystalline material) from the orientation of its structural units and the intrinsic mechanical anisotropy of the structural unit is discussed in relation to the transformation of the orientation distribution function, i.e., mutual conversion of the coefficients in the expansion of the distribution function between the two sets of Cartesian coordinates. The procedure is extended to a two-phase systems (semicrystalline polymers) containing structural units composed of crystalline and noncrystalline materials in three different geometrical arrangements.     

General description of orientation factors in terms of expansion of orientation distribution function in a series of spherical harmonics

A mathematical representation of orientation distribution of structural units within the bulk polymer is given in terms of an expansion of the distribution function in a series of spherical harmonics. Each coefficient of the expanded series is discussed in general relation to the orientation factors, average degrees of orientation distribution, defined by several different authors independently. Several optical techniques to evaluate the orientation factors, the second and fourth moments of orientation distribution of crystalline and noncrystalline structural units from optical dichroic quantities, are discussed. Some graphical representations of the state of orientation are proposed, and the estimation of orientation distribution from the orientation factors of different orders is discussed quantitatively.     

Second harmonic generation and optical anisotropy of a spin-cast polymer film

The nonlinear susceptibilities (χ⁽²⁾₃₃, χ⁽²⁾₃₁), and the refractive index anisotropy, of a main chain accordion polymer, BCSC (see the text for the complete chemical formula), have been measured by the techniques of second harmonic generation (SHG) and waveguiding. A large birefringence, which is induced in the BCSC film by the spin-coating process, is almost removed by electric field poling. Our results demonstrate the fundamental difference between the birefringence associated with quadrupolar orientational order and the dipolar order associated with SHG. © 1993 John Wiley & Sons, Inc.     

Quantitative nanoorganized structural evolution for a high efficiency bulk heterojunction polymer solar cell

We have developed an improved small-angle X-ray scattering (SAXS) model and analysis methodology to quantitatively evaluate the nanostructures of a blend system. This method has been applied to resolve the various structures of self-organized poly(3-hexylthiophene)/C61-butyric acid methyl ester (P3HT/PCBM) thin active layer in a solar cell from the studies of both grazing-incidence small-angle X-ray scattering (GISAXS) and grazing-incidence X-ray diffraction (GIXRD). Tuning the various length scales of PCBM-related structures by a different annealing process can provide a flexible approach and better understanding to enhance the power conversion of the P3HT/PCBM solar cell. The quantitative structural characterization by this method includes (1) the mean size, volume fraction, and size distribution of aggregated PCBM clusters, (2) the specific interface area between PCBM and P3HT, (3) the local cluster agglomeration, and (4) the correlation length of the PCBM molecular network within the P3HT phase. The above terms are correlated well with the device performance. The various structural evolutions and transformations (growth and dissolution) between PCBM and P3HT with the variation of annealing history are demonstrated here. This work established a useful SAXS approach to present insight into the modeling of the morphology of P3HT/PCBM film. In situ GISAXS measurements were also conducted to provide informative details of thermal behavior and temporal evolution of PCBM-related structures during phase separation. The results of this investigation significantly extend the current knowledge of the relationship of bulk heterojunction morphology to device performance.     

Investigations of optical anisotropy at polymer surfaces and in thin polymer films by variable angle ellipsometry

Summary Variable angle ellipsometry has been used to study laterally homogeneous, interfacial structures whose index of refraction varies only in the normal direction. A polyimide film (1.4 m thick) was studied on glass and the thickness and the indices of anisotropy n and n perpendicular and parallel to the lateral plane determined with high precision. Better fits to experimental data were obtained by assuming an additional thin layer, with different film parameters, at the polymer/substrate interface.     

Determination of transition moment directions by means of dichroic spectra in stretched polymer films. Mechanism of solute orientation

The orientation of planar molecules in stretched polymer films has been studied by means of absorption spectroscopy with linearly polarized light. Solute orientation was considered as a function of the solute structure, polymer structure, polymer orientation and of the temperature. We conclude that orientation of the solute cannot derive primarily from attractive interactions between solute and polymer matrix.     

Polarization dependence of Raman scattering from a thin film involving optical anisotropy theorized for molecular orientation analysis

Polarized Raman scattering from a thin film involving uniaxial optical anisotropy deposited on a dielectric substrate has analytically been theorized. The analyte film is modeled as a three-phase system (air/film/substrate) to calculate the electromagnetic fields of the incident and scattered light propagating across the system with an aid of the transfer matrix method to exactly take the optical anisotropy of the film into account. On the new theory, a methodology for molecular orientation analysis of an extended polymethylene chain in the film is proposed, which is employed for determination of the tilt angles of the chains in single- and five-monolayer Langmuir-Blodgett (LB) films of cadmium stearate deposited on a glass plate. The results agree well with those obtained by infrared spectroscopy, which confirms reliability of the present method.     

Investigation of molecular chain orientation change of polymer crystals in phase transitions by friction anisotropy measurement

Direct observation of the molecular orientation change in polymer crystals provides us visible information for understanding their structural phase-transition mechanisms. In this letter, we successfully identified the main-chain orientation of poly(vinylidenefluoride-trifluoroethylene) (P(VDF-TrFE)) crystals over all directions using friction anisotropy measured by lateral-modulation friction force microscopy (LM-FFM). This technique made possible our investigation of molecular orientation changes caused by a ferroelectric phase transition and also a fabrication process for artificial nanometer-scale structures. These results give us visual information that is directly connected to the transition mechanisms.     

High‐accuracy bulk metallic glass mold insert for hot embossing of complex polymer optical devices

Metallic glasses (MGs) have been reported to be excellent mold insert materials for hot embossing of polymers, but limited by the simple shape of the embossed polymer devices and the high cost resulted by the application of Pt‐ and Pd‐based MGs. The development of inexpensive MG mold inserts with complex shape as well as high accuracy is of great importance. In present work, polymethylmethacrylate optic devices with complex micro structures and excellent grating performance have been hot embossed precisely by using newly developed centimeter‐sized Ni₆₂Pd₁₉Si₂P₁₇ MG molds. The Ni₆₂Pd₁₉Si₂P₁₇ MG exhibits high fracture strength of 1840 MPa, distinctive plastic strain of 4% and high thermal‐stability. The die imprinted MG microstructures exhibit very low linear shrinkage (0.002 μm) and relative linear shrinkage rate (0.033%). It indicates that the Ni₆₂Pd₁₉Si₂P₁₇ MG could serve as inexpensive and durable mold inserts for precise embossing of polymer micro devices in large scale. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 463–467     

Long time dynamics of a polymer with rigid body monomer units relating to a protein model: Comparison with the rouse model

Simulation data from an off-lattice polymer model are compared with data from the Rouse model. The polymer model is built of sequentially connected rigid monomer units that represent the amide planes of a protein backbone. The time propagation of the dynamics of the polymer model is performed by a Monte Carlo method. The elementary Monte Carlo steps correspond to local confomational changes in a window of three consecutive monomer units. The time autocorrelation functions of end-to-end distances from segments within the linear chain molecule are considered in detail. Both models exhibit a stretched exponential decay pattern. A comparison of the data from the Rouse model and the computer simulation provide an estimate of the time unit of 15 ps for a full scan of the algorithm for local conformational changes along the chain. With a conservative estimate of the parameters governing the Rouse model this time unit is four orders of magnitude longer than the elementary time step of a conventional computer simulation of polymer dynamics based upon the classical equations of motion for all atoms. © 1992 by John Wiley & Sons, Inc.     

Application of geometric algebra for the description of polymer conformations

In this paper a Clifford algebra-based method is applied to calculate polymer chain conformations. The approach enables the calculation of the position of an atom in space with the knowledge of the bond length (l), valence angle (theta), and rotation angle (phi) of each of the preceding bonds in the chain. Hence, the set of geometrical parameters {l(i),theta(i),phi(i)} yields all the position coordinates p(i) of the main chain atoms. Moreover, the method allows the calculation of side chain conformations and the computation of rotations of chain segments. With these features it is, in principle, possible to generate conformations of any type of chemical structure. This method is proposed as an alternative for the classical approach by matrix algebra. It is more straightforward and its final symbolic representation considerably simpler than that of matrix algebra. Approaches for realistic modeling by means of incorporation of energetic considerations can be combined with it. This article, however, is entirely focused at showing the suitable mathematical framework on which further developments and applications can be built.     

Continuous self-avoiding walk with application to the description of polymer chains

We develop the continuous self-avoiding walk (CSAW) methodology for investigating temperature dependent thermodynamic properties of finite polymer chains without imposing a lattice. This leads to a new concept: the free energy theta temperature, T(theta)(F), at which the free energy is proportional to chain length. Above T(theta)(F), the polymer chain-solvent mixture leads to a single phase, whereas below T(theta)(F) the polymer solvent system has a positive surface tension with a tendency to phase separation to form a globular phase. For finite chains this coil-globule transition lies above the geometric theta temperature at which the distribution describes a Gaussian coil. CSAW provides the basis for a new approach to predict globular properties of real polymers.     

Low-temperature dispersion related to methylene units of a polymer main chain

Polymers containing dynamically isolated polymethylene segments of various lengths were obtained from the reaction of bisphenol-A-diglycidyl ether with α,ω-diamines. On the basis of the mechanical damping data of these polymers, it was established that the shortest polymethylene segment to show the ?125°C. γ dispersion, characteristic of polyethylene, must consist of at least five carbon atoms.     

Compliant rubber domains in a rigid polymer matrix: Shape and orientation factors related to cavitation and plastic dissipation

The hydrostatic stress in compliant rubber inclusions embedded in a rigid polymer matrix is evaluated for various shapes and orientations of the rubber domains and triaxialities of the remote stress tensor to determine the propensity of the inclusions to undergo cavitation. The first section analyzes the case of rubber particles of an ellipsoidal shape assuming linear elasticity of the matrix and small strains. It is shown that flat shapes, of which the long axis lies perpendicular to the direction of the maximum principal stress, are subjected to the highest levels of hydrostatic stress. The pressure induced by the deviatoric part of the remote stress tensor in the compliant rubber domains depends strongly on their shape and orientation, whereas the pressure induced by the hydrostatic part of the tensor is almost insensitive to the shape and orientation of the compliant domains. The second section examines the stress concentrations for elastoplasticity and plastic dissipation in the matrix. It is found that spherical inclusions ensure the best compromise between the early occurrence of plasticity and large amounts of plastic dissipation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1476–1486, 2004     

Effect of gamma radiation on the structural and optical properties of Polyethyleneterephthalate (PET) polymer

Effect of 1.25 MeV gamma radiation on the structural and optical properties of virgin and gamma irradiated (0-2000 kGy) Polyethyleneterephthalate (PET) polymer samples are analyzed using powder X-ray diffractometer and UV-vis spectrophotometer. Diffraction pattern of PET polymer indicates the semi-crystalline in nature whereas the crystallinity increases with increasing dose of irradiation. The remarkable variation in crystallite size is also observed. The absorption and activation energy increase and the optical band gap (E_g) decreases with increasing dose in UV-vis studies. The existence of the maximum absorption, their shifting and broadening due to gamma irradiation in PET polymer are also discussed.     

Crystal orientation in a semicrystalline polymer in relation to deformation of polymer spherulites. IV. Crystal orientation mechanism of nylon-6 under uniaxial stretching

A model relating crystal orientation to the deformation of nylon-6 spherulites under uniaxial stretching is discussed in terms of the orientation distribution functions of reciprocal lattice vectors of crystal planes, such as the (002) and (200) planes. The distribution functions calculated from the model are compared with those obtained from x-ray diffraction experiments. It is found that the crystal a axis and, consequently, the direction of hydrogen bonds within the crystal (α modification) orient parallel to the lamellar axis in the undeformed state, and that the crystal orientation behavior of nylon-6 is much different from that of low-density polyethylene, being characterized by much smaller values of the reorientation parameters of crystallites within orienting lamellae. Moreover, small-angle light scattering for H_v and V_v polarization is also calculated on the basis of the spherulite deformation model by taking the nylon-6 crystal as having orthogonal–biaxial symmetry in optical anisotropy. It is concluded that the H_v scattering can be realized in terms of the proposed model for spherulite deformation by taking into account a considerable contribution of hydrogen bonds to the molecular polarizability, so as to make the polarizability along the crystal a axis larger than that along the b axis. In other words, this conclusion suggests positively birefringent spherulites in the nylon-6 samples studied.