Molecular orientation in poly(vinyl chloride) studied by Raman spectroscopy and birefringence measurements

The ratios of the intensities of Raman scattering in the C? CI stretching region for eight combinations of sample orientation and directions of polarization of incident and scattered light have been measured for 15 samples of poly(vinyl chloride) (PVC) containing 0, 5, 10, 15 or 20 pph dioctyl sebacate (DOS) plasticizer which had been drawn uniaxially at 22, 70, 75, 80, or 90°C to draw ratios in the range 1–4.5. The birefringences of the samples were also measured. The Raman data were analyzed to give 〈P₂(cosθ)〉_cryst and 〈P₄(cosθ)〉_cryst, the values of the second- and fourth-order Legendre polynomials in cosθ averaged over the distribution of orientations of the crystallites, where θ is the angle between the c axis of a typical crystallite and the draw direction. Comparison of 〈P₂(cosθ)〉_cryst with the birefrigence showed that the crystallites are more highly oriented than the noncrystalline material in samples containing the higher amounts of plasticizer drawn at the higher temperatures. A value of 13.0 × 10^?3 was deduced for the birefringence of fully oriented PVC. The values of 〈P₄(cosθ)〉_cryst for a given 〈P₂(cosθ)〉_cryst were found to be higher than predicted by calculations based on two simple models, the pseudoaffine rigid-rod rotation model and the affine rubber elasticity model.     

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.     

Orientation of uniaxially stretched poly(ethylene naphthalene 2,6‐dicarboxylate) films by polarized infrared spectroscopy

Poly(ethylene naphthalene‐2,6‐dicarboxylate) has been uniaxially stretched at different draw ratios and at two different temperatures below and above its glass transition (T_g ～ 120 °C) respectively, at 100 and 160 °C. Crystallinity has been evaluated from calorimetric analyses and compared to the values deduced by FTIR spectroscopic data. As expected, the obtained results are quite similar and show that films stretched at lower temperature (100 °C) are more crystalline than those stretched at 160 °C. Optical anisotropy associated with orientation has been evaluated by birefringence and show that films stretched at 100 °C are more birefringent than those stretched at 160 °C as a result of a higher chain relaxation above T_g. Polarized FTIR was also performed to evaluate the individual orientation of amorphous and crystalline phases by calculating dichroic ratios R and orientation functions 〈P₂(cos θ)〉 and also show that amorphous and crystalline phases are more oriented in the case of films stretched below T_g. Nevertheless, the orientation of the amorphous phase is always weaker than that of the crystalline phase. Films stretched at 100 °C show a rapid increase in orientation (and crystallinity) with draw ratio and 〈P₂(cos θ)〉 reaches a limit value when draw ratio becomes higher than 3.5. Films drawn at 160 °C are less oriented and their orientation is increasing progressively with draw ratio without showing a plateau. A careful measurement of the IR absorbance was necessary to evaluate the structural angles of the transition moments to the molecular chain axis. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1950–1958, 2007     

Study of crystalline orientation in drawn ultra-high–molecular weight polyethylene films

A wide-angle x-ray diffraction (WAXD) study of the development of molecular orientation in the crystalline phase of ultra-high–molecular weight polyethylene films prepared by the gelation–crystallization method is presented. WAXD scans of the undrawn films show that the lamellae are oriented in the plane of the films. Upon drawing at 130°C, the orientation of the molecular chains changes from the direction normal to the film surface (ND) to the elongation direction. The decrease of the 200/020 intensity ratio at low draw ration (λ <10) indicates that double orientation develops during the transformation from the lamellar to the fibrillar morphology, with the a-axis oriented parallel to ND. The orientation distributions of the 110, 200, 020, and 002 planes of the orthorhombic unit cell of polyethylene were studied and characterized by the coefficients of a Legendre polynomial series. At a draw ratio of 4.5, the second-order coefficient, 〈P₂(cos χ〉, already gets close to its limiting value, but it is shown that higher order coefficients of the polynomial series can be used to describe the evolution of the orentation, even up to λ = 50. The coefficients relative to the molecular chain orientation, 〈P_n(cos χ)〉_c, can be calculated from different crystalline reflections. Curve-fitting calculations were made in order to improve the correlation between the results obtained from the orientation distribution of the 110, 020, and 002 planes. A Person VII function was found to give a better fit of the experimental curves than Gaussian or Lorentzian equations. © 1993 John Wiley & Sons, Inc.     

General description of optical dichroic orientation factors for relating optical anisotropy of bulk polymer to orientation of structural units

The relationship between the optical anisotropy of high polymeric materials in bulk and the orientation of structural units within the materials was described in general by using several types of mean values of the orientation distribution function of three Eulerian angles, i.e., the orientation factors, under some assumptions about the symmetry of the function being applicable for the most of the industrial products. A newly defined biaxial orientation factor, F_θηⁱ = 〈sin² θ_j cos 2η_j〉, where θ_j and η_j are the polar and azimuthal angles of the jth axis within the structural unit with respect to the bulk axes, may relate the biaxial orientation of the structural units to the dichroic orientation factors, which are measurable optical anisotropic indices of the bulk materials. Some applications of the results to the birefringence and infrared and dye dichroism are also discussed.     

Dynamic Monte Carlo Simulation on the Polymer Chain with One End Grafted on a Flat Surface

A linear polymer chain in good solvent condition with one end grafted on a infinitely large, impenetrable flat surface is investigated using dynamic Monte Carlo simulation on a simple cubic lattice. Chain shape and dimension, angular correlation between the direction of the end‐to‐end vector and that of the longest principal axis of inertia are studied and discussed. Results reveal that the asphericity of end‐grafted polymer chains is greater than that of free ones, the limit ratio 〈L₁²〉 : 〈L₂²〉 : 〈L₃²〉 is about 1 : 3.0 : 14.9. The limit of mean angle 〈θ〉 of end‐grafted chains is about 22°, smaller than that of free chains, indicating angular correlation between the direction of the end‐to‐end vector and that of the longest principal axis is reinforced.     

The oblique chiral nematic phase in calamitic bimesogens

ABSTRACT

The discovery of the oblique chiral (or, the twist-bend, N_TB) nematic phase predicted for bent-core mesogens has engendered much interest due to its unique structure and physical properties, and the possibility of use in the next generation of fast electro-optic technology. Bimesogenic calamitic as well as bent-core mesogens are found to form the N_TB phase. Here, we report direct measurements of the temperature dependence of the conical tilt and the evidence of volcano-like orientational distribution of molecules in the N_TB phase. Optical and x-ray scattering investigations of two single-component calamitic bimesogens and their mixtures show that, while the Maier–Saupe orientational distribution function (ODF) is valid for the higher temperature nematic phase, a generalised expansion in terms of even Legendre functions is needed for the N_TB phase. Temperature dependence of the ODFs and the order parameters 〈P₂(cosβ)〉, 〈P₄(cosβ)〉, and 〈P₆(cosβ)〉 has been measured in both phases. The parameters 〈P₂(cosβ)〉 and 〈P₄(cosβ)〉 increase/decrease in the N/N_TB phase with decreasing temperature, while 〈P₆(cosβ)〉 remains vanishingly small for all samples. The value of 〈P₄(cosβ)〉 becomes negative in the N_TB phase confirming a conical distribution of molecules as they follow a helical trajectory keeping the local director tilted at an angle α wrt the macroscopic director. The heliconical tilt calculated from ODFs, exhibits a power law behaviour with temperature, vanishing at the transition to the N phase.     

Anisotropy in the dimensional and elastic parameters of confined macromolecules

Using lattice simulations the effect of confinement on the size, orientation and elastic properties of athermal chains was investigated. For chains confined in a slit or in a “cylinder” with square profile a minimum was observed in the dependence of the mean‐square end‐to‐end distance 〈R²〉 on the plate distance D. However, the components of the mean chain dimensions perpendicular and parallel to the walls, 〈R²_⟂〉 and 〈R²_∥〉, steadily diverge with reduction of the pore size. In a slit the distribution functions of the chain vector perpendicular and parallel to the plates, W〈R²_⟂ 〉 and W〈R²_∥〉, respectively, were computed. The marked difference between these distribution functions is interpreted as a sign of enhanced alignment of chains of the shape of elongated ellipsoids along the pore walls. A major part of the free energy of confinement ΔA_cf stems from this mechanism of pore‐induced macromolecular orientation. A striking anisotropy was observed in the elastic free energies A^el_⟂ and A^el_∥ of chains deformed in the direction perpendicular and parallel to the walls and in the corresponding force‐displacement functions. Finally, the relation between the elastic free energy A^el and the free energy of confinement ΔA_cf and between the forces f and f_solv derived thereof is analysed.     

The Influence of External Electric Field on Local Orientations and Phase Transitions in Polymer Liquid Crystals (PLCs)

The starting point is our previous study of influence of the internal molecular mean field of dipole‐dipole interactions on local orientation and phase transitions in polymer liquid crystal (PLC) systems of longitudinal chains.^{[1, 2]} Electric dipoles are created by LC mesogen moieties. The longitudinal PLC is a macromolecule of consecutively copolymerized LC and flexible polymer sequences. We now amplify the model by inclusion of dipole‐external electric field interactions. We find that the external fields can seriously modify the local orientational order of the system and affect phase transition parameters dependent on that order. In particular, the external fields induce the formation of disoriented nematic phases with negative values of the second order orientation parameter 〈P₂〉 for LC sequences in the longitudinal PLCs while the first order parameter 〈P₁〉 is positive. However, some rapid decreases in 〈P₁〉 are observed at points of positive‐to‐negative transitions of 〈P₂〉; thus the LC disorientation manifests itself. The limiting case of the monomer liquid crystal (MLC) systems is included also.     

Elastic modulus and atomic displacements of skeleton and side groups in stretching of a polymer chain

We propose a new method of calculating elastic modulus and atomic displacements of a stretched polymer chain. We use a stretched Cartesian coordinate system and a stretched B matrix defined by the Cartesian displacement components of the bonds to express the potential energy matrix F_x for stretching. The method is used to calculate elastic moduli of planar-zigzag-chain vinyl polymers and helical-chain isotactic polypropylene and the atomic displacements of their skeleton and side groups. The skeletal displacements of planar-zigzag-chain polymers are about ten times larger than those of the side groups and reverse displacements of the two adjacent skeletal units occur in the direction perpendicular to the stretching direction along the fiber axis. In the case of isotactic polypropylene, the methyl group has more effect than the torsional change around the C? C bond on the skeletal deformation. © 1993 John Wiley & Sons, Inc.     

Elastic behavior of single polymer chains adsorbed on rough surfaces

In this paper, elastic behaviors of single polymer chains adsorbed on the rough surfaces with a substrate and some periodically tactic pillars are investigated by the pruned-enriched-Rosenbluth method (PERM). In our simulation, a single polymer chain is firstly adsorbed on the substrate and then pulled along the z-axis direction, which is vertical to the substrate. We investigate the chain size and shape of polymer chains, such as mean-square radii of gyration per bond 〈S²〉_xy/N, 〈S²〉_z/N and shape factor 〈δ^∗〉 in order to show how the size and shape of adsorbed polymer chains change during the desorption process. Due to the occurrences of separation of the chains from the substrate, farther adsorption on the upper surfaces of pillars and complete separation from the whole rough surfaces in the elastic process, the changes of 〈S²〉_xy/N, 〈S²〉_z/N and 〈δ^∗〉 during the process are complicated. On the other hand, some thermodynamic properties such as average energy per bond, average Helmholtz free energy per bond, elastic force f are investigated, and our aim is to study the elastic behaviors of polymer chains adsorbed on the rough surface during the elasticity process. Elastic force f has some plateaus during the desorption process for strong adsorption interaction. If there is no adsorption interaction, the chains can get away from the rough surfaces spontaneously. These investigations can provide some insights into the elastic behaviors of polymer chains adsorbed on the rough surface.     

One-dimensional models of polymer dynamics. I. Dashpot-spring models applied to a single rotor

The proposion of Clark and Zimm that a dashpot and a spring can be used in place of a set of rotational barriers in polymer dynamics is studied. The simplest possible case is examined here, that of a single rotor. Reasons for altering the Clark–Zimm diffusion equation are presented and an alternative diffusion equation is proposed. The results of both diffusion equations for the correlation function 〈exp[?iθ(0)] exp[iθ(t)]〉 (θ is the angular position of the rotor) are compared with the correlation function for a rotor in an n-fold cosine potential. Although the two diffusion equations differ, both agree well with the n-fold cosine model for barriers above a few k_BT. This agreement is obtained in the absence of adjustable parameters, and motivates the application of these two diffusion equations to polymeric systems.     

Headgroup hydration in egg-lecithin multibilayers affects the behaviour of DPH probes

Angle-resolved fluorescence depolarization experiments were carried out on DPH molecules embedded in egg-licithin bilayers of different water contents. It was found that the order parameter 〈P₂〉 of the absorption moment is significantly higher than that of the emission moment and that the difference increases on hydrating the lecithin headgroups. The changes in the order parameter 〈P₂〉 and 〈P₄〉 of the DPH molecules induced by hydration are consistent with X-ray diffraction data. Furthermore the reorientational motions of the DPH molecules were found to become faster with increasing hydration.     

Investigation on the potential barrier to internal rotation in molecules——Ab initio calculation and energy partition of the internal rotation barrier in complex molecule H_3N-BH_3

Based on the ab initio/6-31G~* calculation, the potential barrier to internal rotation in mol-ecule H_3N--BH_3 has been studed by means of PD/LSF atomic charge model and Buckingham(exp--6-1)energy partition method. The results indicate that the order of the contributions of the componentsto the total energy barrier △E is |△V_(es)|(electrostatic) >|△V_(et)| (charge transfer)>|△V_(ex)| (exchangerepulsion)>|△V_(di)| (dispersion). For △V_(es) there are maxima at θ= 30°and 90°, and a saddle atθ= 60°. There are good linear relationships for the total barrier △E, △V_(ex) and △V_(di) with cos3θrespectively, and the same for the dipole moment from PD/LSF model (μ_(PD)) and that from abinitio calculation (μ_(QM)) vs. cos3θ respectively.     

Conformation study of poly(p‐dioxanone) fibers by polarized Raman spectroscopy,X‐ray diffraction,and conformation analysis

The molecular orientation distribution of poly(p‐dioxanone) (PPDX) uniaxially oriented commercial fibers was determined by polarized Raman spectroscopy and X‐ray diffraction. The order parameters 〈P₂₀₀〉 and 〈P₄₀₀〉 of the orientation distribution function were determined by polarized Raman spectroscopy. For the C?O stretching band, the values of 〈P₂₀₀〉 and 〈P₄₀₀〉 obtained are equal to ?0.40 ± 0.04 and 0.28 ± 0.04, respectively. These results clearly indicate that the carbonyl groups are highly oriented perpendicular to the fiber axis. X‐ray diffraction led to a fiber repeat value of 0.628 nm for these samples, and to 〈P₂₀₀〉 and 〈P₄₀₀〉 values of 0.93 and 0.82, respectively, for the c‐axis orientation, indicating a high orientation in the draw direction of the fibers. A Monte‐Carlo conformational search led to 20 low‐energy conformations, but only one of these was found compatible with both the fiber repeat and the angle between the C?O bond and the fiber axis. This conformation, a 2₁ helix with a tg^?ttg^? succession of torsion angles, is proposed as the existing conformation in the crystalline state. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 406–417, 2008     

Studies of micro-brownian motion of a polymer chain by the fluorescence polarization method. I. Fluorescent conjugates of polyacrylamide

Polyacrylamide having a fluorescent residue at the chain end was prepared by polymerization of acrylamide in the presence of a fluorescent dye. The segmental motion of the chain end in dilute solution was studied by the fluorescence polarization method on the fluorescent polyacrylamide conjugates thus obtained. The linear relation between 1/p and T/η₀ held for every sample studied in aqueous media, where p is the degree of polarization of the fluorescence, T is the absolute temperature, and η₀ is the viscosity of the medium. The mean relaxation time 〈ρ〉 of the conjugate was evaluated from these data as a function of the molecular weight of the conjugate. The value of 〈ρ〉 increased slightly with molecular weight, varying from 3.3 × 10^?9 to 7 × 10^?9 sec. The absolute values of 〈ρ〉 and its molecular weight dependence suggest that 〈ρ〉 represents the mean rotational relaxation time for the cooperative motion of about ten monomeric units at the chain end. The effect of the mean extension of polymer chain on the segmental motion was found to be negligible.     

A molecular study on the reinforcement of polymethylene elastomers

Monte Carlo simulations are carried out on filled networks of polymethylene (PM), which are modeled as composites of PM chains and three-dimensional cubic lattices of filler particles. Calculations are carried out for PM chains with various chain lengths n and various cubic unit dimensions a. The elastic behavior is investigated by using a realistic rotational-isomeric-state (RIS) model and enumeration calculation method. The average conformations, such as a priori probability P_η and the segmental orientation function 〈P₂(cosζ)〉 of PM chains are also calculated. In the process of tensile deformation, the a priori probability P_t increases with elongation ratio λ, however, it decreases with increasing cubic unit dimensions a. The segmental orientation distribution function 〈P₂(cosζ)〉 of deformed PM chains decreases with increasing cubic unit dimensions a, especially in the region of large deformation. Average Helmholtz free energy per bond becomes small when increasing cubic unit dimensions a, and average energy per bond becomes large when increasing cubic unit dimensions a. We find that the elastic force increases with elongation ratio for small λ, and abruptly for large λ. In the meantime, the energy contribution to elastic force is negative and significant. It is also shown that the elastic force and the energy contribution to elastic force is almost the same with various cubic unit dimensions a. The ratio f_u/f ranges from −0.4 to −0.6 at T=425 K. The reinforcement effects on the Helmholtz free energy 〈A〉 and energy 〈U〉 are important; however, the effect on the elastic force is insignificant. Our calculation may provide some insight into the macroscopic phenomena of rubber elasticity.     

Orientation Dependent FT Raman Microspectroscopy on Hemp Fibers

Summary: FT Raman microspectroscopy was used for polarization experiments on strained hemp fibre cells. The cellulosic plant fibers were macerated with alkaline and enzymatic solutions. Those cleaned and refined single fiber cells were subjected to micro tensile tests as well as to polarization measurements under the FT Raman microscope. Mechanical parameters of the fiber cells (e.g. E-modulus) were determined and changes in orientation of the  (C O C) structure units of the cellulose were considered with respect to fiber stress and molecular fiber structures. Intensity ratios R₁ and R₂ calculated on the polarized micro FT Raman spectra of the strained fibers describe the order parameter 〈P₂〉 and 〈P₄〉 allowing the quantitative determination of the orientation of the structure units  (C O C) of fiber cellulose with respect to the fiber cell axis.     

A Monte Carlo Study of the Elastic Behavior of Polymethylene Chains

The rubber elastic behaviors of long polymethylene (PM) chains are investigated using Monte Carlo simulations and considering the rotational‐isomeric‐state model. Through the Monte Carlo method we can generate many PM chains in the equilibrium states, and obtain the average Helmholtz free energy 〈A〉 and average energy 〈U〉. Chain dimensions and thermodynamic statistical properties of long PM chains under various elongation ratios λ are also calculated. We find that the elastic force f increases with elongation ratio λ, and that energy contribution f_u to the elastic force is negative and significant. The ratio f_u /f ranges from –0.37 to –0.32 at T = 300 K and from –0.53 to –0.40 at T = 413 K, and decreases with increasing temperature, which agrees with the experimental data. Our calculations may provide some insights into the macroscopic phenomena of rubber elasticity.     

New aspects of the single phase aggregate model for oriented polymers

A reinvestigation of the single phase aggregate model (SPAM) of Ward applied to the elastic properties of uniaxially oriented polymers is presented. It is shown that the Voigt and the Reuss orientation average of elastic constants can be represented as a linear transformation in a 5-dimensional vector space. The corresponding transformation matrix can be diagonalized, showing that the eigenvalues of this transformation are the orientation parametersP ₀ =1,P ₂ andP ₄ . Taking advantage of this representation an easy test of applicability of the SPAM is proposed. Possibilities to evaluate the SPAM parameters are reviewed.