Variation of crystallite orientation with degree of crystallinity: Isotactic polystyrene

The orientation of the crystallographic c axis (chain axis) was followed by x-ray diffraction during the crystallization of four samples of isotactic polystyrene differing in elongation ratio. The crystallite orientation can be expressed by 〈cos² χ_c〉, where χ_c is the angle between the c axis and the stretching direction. The degrees of crystallinity w were estimated from the diffraction data by using density for calibration. It was found that 〈cos² χ_c〉 decreases in a linear manner with crystallinity, the rate of decrease being very small when the elongation ratio α is 5, but becoming progressively larger as α is decreased toward unity. A qualitative measure suggests that amorphous orientation decreases during crystallization at a rate which is nearly independent of α. The variation of 〈cos² χ_c〉 with w is therefore governed by the orientation of the statistical chain segments prior to crystallization. If the elongation ratio is small, the supply of well oriented statistical segments is limited, and 〈cos² χ_c〉 will decrease at a rapid rate during crystallization. A treatment due to Krigbaum and Roe permits evaluation of the ratio, ν/N, where ν and N are the average numbers of statistical segments in the crystallization nucleus of critical size, and in a network chain, respectively. Our polystyrene samples were not crosslinked, so chain entanglements must serve as junction points. Values of ν could not be obtained, since N was unknown. However, the (ν/N) ratio for isotactic polystyrene decreases slowly with α, and the values agree reasonably well with those obtained in a previous study of oriented polychloroprene networks. After nearly complete crystallization (ω ca. 0.30), the long period spacing measured by low angle diffraction was approximately 135 Å, and varied only slightly with elongation ratio in the range α = 1 to 5. It therefore appears that chain folded lamellae are present in both drawn and undrawn samples of isotactic polystyrene.     

Crystallite orientation in stretched polychloroprene networks. II

The orientation of crystallites grown isothermally in several drawn trans-polychloroprene networks is studied as a function of crystallization temperature t_x, degree of crystallinity ω, and elongation ratio α. The orientation distribution is particularly simple for this polymer since the crystallographic c axis (chain axis) orients preferentially along the stretching direction, while a and b are randomly arranged about c. Hence the parameter cos² χ_c adequately characterizes the distribution, where χ_c is the angle between the c axis and the fiber axis, and the average is taken over all crystallites. A treatment due to Krigbaum and Roe is utilized to obtain values of v (the number of statistical segments comprising the crystallization nucleus of critical size) through comparison of the average orientation of crystallites and amorphous statistical segments. The behavior observed falls into two categories. First, if the initial amorphous network is well oriented, 〈cos² χ_c〉 is independent of crystallinity during both crystallization and melting, and v varies with t_z (or the degree of supercooling) as predicted by nucleation theory. If different networks are to have the same crystallite orientation distribution, they must not only be crystallized at the same supercooling, but must also have the same distribution of amorphous segment orientations. Both the relative elongation and the network crosslink density affect the latter distribution. Next, we consider the second category. If the initial amorphous orientation is poor, 〈cos² χ_c〉 decreases linearly during crystallization and increases along approximately the same path during melting. Further, 〈cos² χ_c〉 for a given t_z yields v values which are too large. These two behaviors can be explained if, in the former case, nucleation involves the best oriented statistical segments of all network chains, while in the latter there is a selection according to the chain displacement vector orientation. Thus, if the amorphous orientation is poor, both the orientation and thermodynamic stability of the crystallites decreases with further crystallization. If this decreased stability is reflected in shorter fold lengths, the reversible variation of long period spacing with temperature reported earlier for an oriented polychloroprene network can also be explained as a preferential melting process.     

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     

Polarized Raman studies of crystalline and amorphous orientation in polyethylene

Polarized Raman intensities have been obtained from thin films of oriented low-density polyethylene (PE) immersed in silicone oil to minimize surface scattering. Studies were made using the 1170 cm^?1 crystalline band and the 1081 cm^?1 amorphous band, and from these the orientation averages 〈cos² θ〉 and 〈cos⁴ θ〉 were calculated. These were found to compare favorably with the values of 〈cos² θ〉 for the polymer chain in the crystalline and amorphous phases obtained from measurements of infrared dichroism. Both orientation averages could be theoretically fitted by using reasonable parameters.     

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.     

Intermolecular interaction and magnetic coupling mechanism of a mixed-valence CuIICuI tetranuclear complex with iodide bridge

A tetranuclear Cu^ICu^II mixed oxidation state complex, [Cu^II ₂(μ-I)₂Cu^I ₂(μ-I)₂(phenP)₂I₂] (phenPE: 2-(1H-pyrazol-1-yl)-1,10-phenanthroline), has been prepared and its crystal structure is determined by X-ray crystallography. In the complex, Cu^II is a distorted square pyramid and Cu^I is a distorted trigonal planar coordination environment; Cu^II and Cu^I are bridged by iodide. It is rare to form a Cu^II-iodide bond and for Cu^II and Cu^I to be bridged by iodide. In the crystal, there is a slipped π–π stacking between adjacent Cu^II complexes, which resulted in the formation of the 1-D chain along the c axis. The fitting for the variable-temperature magnetic susceptibility data gave magnetic coupling constant 2J?=??1.16?cm^?1 and it may be ascribed to the intermolecular π–π magnetic coupling pathway.     

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.     

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.     

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.     

Solution properties of high molecular weight polystyrene

A series of polystyrenes with weight-average molecular weight M?_w up to 1.3 × 10⁷ was prepared by anionic polymerization in tetrahydrofuran (THF). Each sample was characterized by gel-permeation chromatography, light scattering, and viscometry. It was found that each sample had an almost symmetrical and very narrow molecular weight distribution (M?_w/M?_n < 1.07). The mean-square unperturbed radius of gyration 〈S²〉₀ was determined in trans-decalin at 20.4°C as 〈S²〉₀ = 7.8₆ × 10^?18M?_w (cm²). The particle scattering factor was well represented by the Debye equation irrespective of solvent in the range of M?_w < 4 × 10⁶, and only a small deviation was observed in benzene at higher molecular weights. The penetration function Ψ ≡ A₂M²/4π^3/2N_A〈S〉^23/2 was found to approach a relatively low asymptotic value of 0.21–0.23 at molecular weights above 2 × 10⁶ in benzene at 30°C, where A₂ is the second virial coefficient and N_A is Avogrado's number. It was also found that the theta temperature in trans-decalin was affected by the nature of polymer samples. A difference of about 3°C in the theta temperature was observed between two series of anionic polystyrenes, one prepared in THF and the other in benzene, but there was practically no difference in unperturbed chain dimension.     

Crystal structure of polysulfonamides

Structures of poly(alkylene-1,3-benzenedisulfonamide)s [? HN(CH₂)_mNH? O₂SC₆H₄SO₂? ]_n (PMm: 2 ≤ m ≤ 6) were studied by x-ray diffraction and infrared spectroscopy. The crystal structure of PB6 is monoclinic, space group C2/m? C_2h³, with a = 7.70 Å, b = 7.76 Å, c (molecular axis) = 14.1 Å, and β = 117°. Two mirror-image molecules repeating with two monomeric units in an identity period 28.2 Å occupy the same lattice site with equal probability. The alkylene chains assume the planar zigzag conformation, which is the structure isomorphous with PB4. An intermolecular hydrogen bond is formed between each NH group and one of the two O = S groups of the corresponding SO₂ unit. The c axis tends to tilt from the fiber axis by an inclination angle of about 3° around the b axis.     

Crystal structure of poly-p-xylylene. I. The α form

The molecular conformation and the crystal structure of α-form poly-p-xylylene has been determined by x-ray diffraction. The polymer has a monoclinic unit cell with a = 5.92, b = 10.64, c (fiber axis) = 6.55 Å, and β = 134.7°. Two chains pass through the unit cell, and the space groups is C2/m. The packing fraction is 0.705. One monomer unit makes up the fiber identity period and the internal rotation angles are 0° and 90° for the ? CH₂? CH₂? and ? CH₂? ?? bonds, respectively. All benzene rings are in parallel orientation, perpendicular to the ac plane.     

Computer simulation of brownian motion of a polyelectrolyte molecule (charged bead-spring model)

A Langevin equation of motion for a charged bead-spring statistical chain is written in difference form and the relaxation and equilibrium behavior of the chain is studied by computer simulation. Results are presented for the behavior of end-to-end length h, principal axes of the polymer ellipsoid L₁, L₂, L₃, and chain contour length c in terms of their averages, root mean square values, root mean square fluctuations, orientations, and relaxation strengths and times. The simulation was made with various sets of parameters, bead number N, charge on the bead q, and radius of ion atmosphere around the bead k^?1. It is found that 〈h²〉^1/2 and 〈L₁²〉^1/2 increase more strongly with increasing q and decreasing κ than 〈L₂²〉^1/2, 〈L₃²〉^1/2, and 〈c₁²〉^1/2, indicating that the chain is expanded in three dimensions and at the same time is extended along the end-to-end direction. The relaxation time τ_rot of rotation of the end-to-end vector, which is proportional to N² at q = 0, increases with increasing q and tends to be proportional to N³ for an extended chain, while the relaxation time τ_conf of the magnitude of h is almost independent of q and is always proportional to N². It is concluded that the extended chain possesses a well-defined end-to-end axis and the chain rotates as a whole with a relaxation time τ_rot which is much longer than τ_conf. The complex viscosity of the chain is calculated from the Fourier transform of the time–correlation function of momentum flux and is found to have a frequency spectrum similar to that observed for aqueous solutions of poly(acrylic acid). The dominant mode appearing in the low-frequency range is evidenced to arise from the rotation of the extended chain.     

Determination of chain stiffness and polydispersity from static light-scattering

Chain stiffness is often difficult to distinguish from molecular polydisperity. Both effects cause a downturn of the angular dependence at large q² (q = (4π/λ)sin θ/2) in a Zimm plot. A quick estimation of polydisperity becomes possible from a bending rod (BR) plot in which lim (c → 0) qRθ/Kc is plotted against q(〈S²〉_z)^1/2 = u. Flexible and semiflexible chains show a maximum whose position is shifted from u_max = 1.41 for monodisperse chains towards larger values as polydispersity is increased, while simultaneously, the maximum height is lowered. Stiff chains display a constant plateau at large q, its value is πM_L where M_L is the linear mass density. Using Koyama's theory, the number of Kuhn segments can be determined from the ratio of the maximum height to the plateau height, if the polydispersity index z = (M_w/M_n ? 1)^?1 is known. Thus, if the weight-average molecular weight M_w, is known, the contour length L_w, the number of Kuhn segments (N_k)_w, the Kuhn segment length l_k and the polydispersity of the stiff chains can be determined. The influence of excluded volume is shown to have no effect on this set of data. The reliability of this set can be cross-checked with the mean-square radius of gyration 〈s²〉_z which can be calculated from the Benoit-Doty equation for polydisperse chains. Rigid and slightly bending rods exhibit no maximum in the BR plot, and the effect of polydispersity can no longer be distinguished from a slight flexibility if only static scattering techniques are applied.     

Evaluation of the orientation coefficient for the c axis in poly(ethylene terephthalate) fibers

The literature methods for the determination of the mean of the crystallite orientation distribution for the c axis, that is of the orientation coefficient f_c, for poly(ethylene terephthalate) (PET), based on the azimuthal scan of the (1 05) reflection, are reviewed. These methods appear unsuitable for samples presenting the “tilted orientation”; that is, the molecular chain axis inclined by some degrees with respect to the fiber axis, as frequently occurs for PET fibers. A new method for the determination of f_c for PET, also based on the azimuthal scan of the (1 05) reflection (which can be applied also to samples with “tilted orientation”), is proposed. This method implies as a first step the determination of the tilt angle, for which the complete fiber pattern is required. A possible simplifying assumption, which allows use of the sole azimuthal (1 05) profile and makes the method also applicable to poorly oriented samples (for which the determination of the tilt angle is not easy), is also discussed. © 1995 John Wiley & Sons, Inc.     

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     

Synthesis, vibrational spectra, and crystal and molecular structure of 1,5-bis[2-(dihydroxyphosphinyl)phenoxy]-3-oxapentane dihydrate [(HO)2(O)P(C6H4)(OCH2CH2)2O(C6H4)P(O)(OH)2(H2O)] · H2O

A modified method of synthesis of a phosphoryl podand, 1,5-bis[2-(dihydroxyphosphinyl)phenoxy]-3-oxapentane (L), has been developed. The IR spectra of this podand and its dehydrate (L [L · H₂O] · H₂O (I) have been studied, the structure of I has been determined by X-ray crystallography. The crystals are orthorhombic, a = 9.4006(19) ?, b = 25.494(5) ?, c = 8.4264(17) ?, V = 2019.5(7) ?³, Z = 4, space group Pna2₁, R = 0.0512 for 3016 reflections with I > 2σ(I). Compound I is a host-guest molecular complex. Phosphoryl podand L acts as a host molecule, and one of the water molecules (H₂O(11)) is a guest. This molecule forms one donor and one acceptor intramolecular hydrogen bond with hydroxyl groups of two phosphoryl groups (O(8)H(4) and O(3)H(2)) and combines them into an 18-membered macrocyclic ring, acting as a kind of “lock.” The H₂O(11) molecule forms a second donor intramolecular hydrogen bond with the O(5) ether atom. The neutral molecular complexes are linked by hydrogen bonds directly and through the second water molecule (H₂O(10)) into chains running along the c axis.     

Intermolecular interaction and magnetic coupling mechanism of a 2-D mixed-valence CuIICuI coordination polymer containing μ 1,1,3-SCN bridge

A 2-D Cu^ICu^II mixed oxidation state coordination polymer, [Cu^IICu^I(μ _1,3-SCN)₂(μ _1,1,3-SCN)(PhenE)] _n (PhenE: 2-ethoxy-1,10-phenanthroline), has been prepared and its crystal structure determined by X-ray crystallography. In the polymer, Cu^II is a distorted trigonal bipyramidal geometry and Cu^I has distorted tetrahedral coordination. Thiocyanate bridges in two modes, μ _1,3-SCN and μ _1,1,3-SCN, resulting in a 2-D coordination sheet. The crystal structure analysis shows that there is a splipped π–π stacking in the sheet. The fitting for the variable-temperature magnetic susceptibility data gave the magnetic coupling constant 2J?=??2.72?cm^?1 and zJ′?=??2.07?cm^?1. The magnetic interaction may be mainly ascribed to intermolecular π–π magnetic coupling.     

Light scattering study of an aromatic polyamide-hydrazide polymer

The aromatic Polyamide-hydrazide, Monsanto X-500, has been studied by light scattering in dimethyl sulfoxide, a thermodynamically good solvent. The unperturbed dimensions, (〈r〉_av/M)^1/2 = 1.93 × 10^?8 at 25°C., indicate a rather highly extended chain. The persistence length falls in the range 35–63 Å, which corresponds to a length of between two and four formula units. This is considerably smaller than the values which have been reported for the aromatic polyamides, poly(p-benzamide) and poly(p-phenylene terephthalamide). X-500 appears to approximate coil-like behavior at a molecular weight of 45,000. Theoretical predictions, based upon the 〈r〉_av/bL ratio, are compared with the observation that no evidence for an anisotropic phase has been found in X-500 solutions in dimethyl sulfoxide at polymer volume ranging from 0.12 to 0.19 (depending upon the concentration of added LiCl).