Nuclear magnetic relaxation and molecular motion in poly(vinylidine fluoride)

Pulsed NMR T₁, T₂, and T_1ρ measurements are reported for poly(vinylidine fluoride) (PVF₂). The results demonstrate clearly the presence of four relaxation processes, three amorphous and one crystalline. The α relaxation is undoubtedly a crystalline one, while β and γ are both amorphous, in agreement with earlier conclusions from dielectric and dynamic mechanical measurements. The fourth relaxation (β′) observed initially in the mechanical measurements of Kakutani, but undetected in dielectric experiments, has been confirmed in our results and the process is described by an activation energy of 15.1 kcl/mole. Motion of folds on the surface of crystal lamellae is deemed to be the responsible mechanism for the β′ relaxation. Two models have been considered in the interpretation of the α process; rotation of crystalline chains in the vicinity of defects and rotational oscillation of restricted amplitude of all crystalline chains about the main chain axes. Rotation of amorphous chains is a possible mechanism for the γ process while motions of a general nature are responsible for the β relaxation. Our experimental results again indicate that spin diffusion plays an important role in the overall NMR response of the polymer.     

NMR study of molecular motion in oriented long-chain alkanes. II. Oriented mats of polyethylene single crystals

Measurements of the NMR second moment of a uniaxially oriented sample of polyethylene single crystals in the range of temperatures from ?196°C to 130°C and its dependence on the alignment angle γ between the orientation axis (preferential direction of the molecular chains) and the NMR magnetic field are presented. The experimental results are discussed mainly with respect to the high temperature relaxation, called the α process, in polyethylene. They are compared to theoretical predictions made for a number of mechanisms of molecular motion in Part I of this work. Only one of the mechanisms considered is found to be in quantitative agreement with experiment, the mechanism here referred to as flip-flop motion. This consists of thermally activated rotational jumps of the crystalline chain segment between folds around its axis between two equilibrium sites in the lattice. Each rotational jump through 180° is accompanied by a shift of the molecule along its axis by one CH₂ group. The discussion of the low-temperature relaxation of polyethylene, the γ process, is based partly on the above measurements and partly on measurements of second moments for unoriented polyethylene samples varying widely in morphology and noncrystalline content. The decrease of the second moment observed with these samples between ?196°C and 20°C is taken as a measure of the intensity of the γ process. A linear correlation is found between the decrease in the second moment, designated ΔS, and the noncrystalline content, 1 ? α_m; this can be represented by ΔS = 1.4 + 22.1(1 ? α_m). It is shown that neither the crankshaft mechanism not the kink mechanism is able to account quantitatively for this result. The model of a chain end moving in a vacancy fails to adequately describe the angle dependence of ΔS in oriented polyethylene single crystals. The “sandwich model” of a polyethylene single crystal, in which the crystalline core is covered by noncrystalline surface layers, is in better agreement with observations.     

Crystal morphology of the γ (triclinic) phase of isotactic polypropylene and its relation to the α phase

γ-phase crystals of isotactic polypropylene (iPP) obtained from low-molecular-weight extracts of pyrolyzed polymers are examined by electron microscopy and electron diffraction. γ-phase crystals differ from α-phase crystals in three important respects: (i) they are elongated along the b^* rather than the a^* axis, (ii) the chain axis is inclined at 50° to the lamellar surface (indexed as 101) rather than normal to it, and (iii) they show screw dislocations, while α crystals do not. γ crystals are nucleated on the lateral (010) faces of a α crystals; the b_α and b axes are parallel. Virtually no nucleation of the α phase takes place on the γ phase, which is therefore not involved in the repetitive lamellar branching leading to iPP quadrites. Crystallization of the γ phase appears to be favored by or linked to the absence of chain folds and may be involved in the macroscopic curvature of iPP branches.     

Dielectric and rheo-optical properties of some ethylene-carbon monoxide copolymers

Studies were made on films of copolymers of ethylene with 0.5 and 1.0 mole-% carbon monoxide. The carbon monoxide appeared negligibly to affect the degree of crystallinity, melting point, morphology, and dynamic mechanical spectra. Infrared dichroism showed that the orientation of the carbonyl groups was comparable with that of the crystalline CH₂ groups and indicated that the carbonyl groups are at least partially within the crystals. This is confirmed by x-ray measurements which indicate an expansion of the a-axis spacing and by an appreciable increase in the height of the α dielectric loss peak which has been assigned to crystalline motion. This α loss peak moves to a lower temperature with increasing carbonyl content, while the γ dielectric loss peak moves to higher temperatures. Activation energies of 25, 35, and 15 kcal/mole for the α, β, and γ peaks, respectively, were independent of carbonyl content and comparable with values for oxidized polyethylene.     

A dielectric study of chain motions in poly(vinyl methyl ether)

The dielectric permittivity and loss of poly(vinyl methyl ether) (mol. wt. 30,000) have been measured from 12 Hz to 100 kHz at temperatures from 77 K to 320 K. Two relaxation processes, γ and β, are observed at T < T_g (245 K), and one above T_g. The Arrhenius plots of the γ and β processes have activation energies of 20 and 41 kJ mole^?1 respectively. The relaxation rate of the α process is described by the Vogel-Fulcher-Tamman equation or the William-Landel-Ferry equation. The relaxation rates of γ and β processes evaluated from the isochrones differ from those evaluated from the isothermal spectrum. The features of chain motions observed are similar to those in other polymer and rigid molecular glasses.     

The glass transition in linear low density polyethylene determined by thermally stimulated depolarization currents

New thermally stimulated depolarization currents (TSDC) results on LLD polyethylene functionalized with diethylmaleate polar groups are precisely computer fitted with the direct signal analysis technique. It is shown that the TSDC spectrum consists, with increasing temperatures, of a sub-γ peak, a sharp γ peak, and a β and an α relaxation. The first peak is analyzed in terms of Arrhenius relaxation times, whereas the γ and β transitions could only be fitted by using Vogel-Fulcher temperature dependence for the relaxation times. The best value for T_o obtained from both fittings is 69.7 K. This is a quantitative proof for the identification of the γ transition as one of the dielectric manifestations of the glass-rubber transition for polyethylenes, T_g = 136.5 K, which has been discussed extensively in the literature. The β relaxation, T_gβ = 237 K, has also the expected characteristic of a glass transition; the existence of two T_gs in polyethylene could explain our results. © 1996 John Wiley & Sons, Inc.     

Comparative study of dielectric,mechanical, and nuclear magnetic relaxations in linear polyethylene. II. Relaxation spectroscopy of the α, β, and γ loss bands with special emphasis on fine structure

Dielectric, mechanical, and NMR retardation (correlation) spectra for relaxations in linear polyethylene were calculated in normalized form and intercompared. For each of the two local-mode relaxations in the γ region, called γ₁ and γ₂, these spectra are found to be in excellent agreement. For the α region, the spectra for two mechanical processes, called α₁ and α₂, two NMR processes, called α′ and α, and one dielectric process α were calculated. Excellent agreement is found between the spectra for the dielectric α and NMR α′ processes and also spectra for the mechanical α₂ and NMR α processes, due to molecular motion in the interior of crystals. However, the spectrum for the mechanical α₁ process is different from that for the dielectric α and NMR α′ processes, though the activation energy for the first process is almost the same as for the other two. This behavior is interpreted on the assumption that the dielectric α and NMR α′ processes are caused by molecular motion in lamellar surface layers while the mechanical α₁ process is due to grain-boundary slip with viscous resistance of the surface layers in the boundaries. The shapes of the spectra, including the spectrum for the β process, are not affected by diluent.     

Thermal analysis and X‐ray scattering study of metallocene isotactic polypropylene prepared by partial melting

In this study, we examine the effects of heating, nucleation, cooling, and reheating on the thermal properties and structure of metallocene isotactic polypropylene (m‐iPP) that had been prepared initially in a standard state containing nearly equal amounts of the crystallographic α and γ phases. Heat treatment was achieved through partial melting and annealing by the heating of samples to self‐nucleation temperatures (T_n's) that spanned and exceeded the entire range of melting of the standard state, from 122 to 160 °C. The relative amounts of α and γ crystals are determined from the area under the unique wide‐angle X‐ray reflections. The lower and upper endotherms are caused by the melting of γ and α crystals, respectively. Four distinct regions of T_n were identified on the basis of the thermal and structural parameters of m‐iPP. In region I, T_n is below the peak melting temperature of the γ phase. Here, γ crystals are annealed and α crystals are barely affected by T_n. In region II, T_n is above the peak of the lower endotherm but below the peak of the upper endotherm. γ crystals melt, and α crystals anneal. In both regions I and II, the portion of the sample melted at T_n recrystallizes epitaxially with existing parent α lamellae as the substrates, and the amount of α always exceeds the amount of γ. In region III, T_n is above the peak of the upper endotherm, and all γ crystals and some or all α crystals are melted at T_n. The number of α‐crystal nuclei steadily decreases as T_n increases, causing systematic depression of the crystallization and melting temperatures seen during cooling. Finally, in region IV, T_n exceeds the upper endotherm, and only small self‐nuclei or heterogeneous nuclei remain. Recrystallization is now suppressed to lower temperatures. For regions III and IV, a crossover behavior in the relative amounts of α and γ is observed during cooling from T_n. Because of the effective nucleating ability of α toward γ, as the temperature drops, the amount of γ increases and then exceeds the amount of α. With subsequent reheating, the reverse crossover occurs because of the lower melting point of γ. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1644–1660, 2002     

Structural studies of polyethers. IX. Planar zigzag modification of poly(ethylene oxide)

A new crystal modification was found in poly(ethylene oxide) stretched about two-fold after necking at room temperature. An x-ray diffraction analysis indicated that the planar zigzag molecule passes through a triclinic unit cell with parameters α = 4.71 Å, b = 4.44 Å, c (fiber axis) = 7.12 Å, α = 62.8°, β = 93.2°, and γ = 111.4°. The space group is P1 ?C_i¹. Packing of the molecule is very similar to that of monoclinic polyethylene.     

Influence of microstructure and semi-crystalline morphology on the β and γ mechanical relaxations of the metallocene isotactic polypropylene

In this work, the characteristics of the β and γ mechanical relaxations, i.e., temperature and relative intensity, of a series of metallocene iPP samples (MPP) are analysed. The hypothesis that the temperature and the intensity of the glass transition (β relaxation) and local sub-T_g motions (γ relaxation) are related mainly to chain parameters and morphology has been corroborated. On the one hand, it has been found a critical average isotactic length (n₁) around 30 propylene units, under which the β and γ dynamics are promoted with respect to the α relaxation. On the other hand, it is apparent that the features which determine the degree of constraint within the inter-lamellar region, i.e., the fraction of low-T_m crystals, drive the relative intensities of the α, β and γ relaxation processes.     

Nuclear relaxation in atactic polystyrenes: T1 and T1ρ measurements

Measurements have been made on a series of linear atactic polystyrenes whose molecular weights range from 900 to 1.8 × 10⁶, where M _w/M _n ? 1.2. Spin lattice relaxation times have been measured in the laboratory frame (T₁) and in the rotating frame (T_1ρ) in the temperature range 90–500°K. Two major relaxation minima were observed in both sets of measurements. The high temperature process corresponds to the glass transition (α process), the position of the minimum depending on the chain length. The low temperature process appears to originate from the n-butyl endgroups in the polymer, its position being independent of chain length while its intensity is inversely proportional to molecular weight. No other minima were observed, in contrast to some other observations made by broadline and pulsed NMR techniques. Relaxation was exponential in all cases except in the region of the high temperature T_1ρ minimum and above. This nonexponential behavior is possibly connected with the transition at T > T_g observed by a number of other techniques and which is thought to correspond to a transition between two types of liquid state. A correlation frequency diagram has been drawn for all the processes observed in polystyrene by other techniques, (α, β, αβ, γ, and δ) which shows that the T₁ and T_1ρ minimum positions correlate well with the α process and that there is a possible contribution to the relaxation due to the γ process on the low temperature side of the α process. At these measurement frequencies the α and β processes are merged into an αβ process. There is no evidence for a contribution from the mechanical δ process. The effect of the endgroups is observed to very high molecular weights (4.98 × 10⁵), and it seems that a three-dimensional diffusion model would be more adequate than the one-dimensional model used to interpret similar behavior of paraffins and polyethylenes. Measurements of T₁ in the low-temperature region would constitute a method for a rough measurement of the molecular weight of these polymers.     

Synthesis and Characterization of Chromium-Based Catalysts for Ethylene-1-hexene Copolymers Preparation via In-Situ Polymerization of Ethylene

The tandem catalysis system including the trimerization catalyst of CrCl₃/SNS (SNS = bis-(2-pentylsulfanyl-ethyl)-amine) (Cat 1) and the copolymerization catalyst Cat 2 of Cr/SiO₂ (Grace 643) has been prepared and used to the synthesis of branched polyethylene. The optimum polymerization conditions were found to be as follows: chromium concentration 0.2 wt %, ethylene pressure 23 bar, solvent hexane, polymerization temperature 90°C, co-catalyst triethylaluminum. The optimally prepared polyethylene was characterized thermally and morphologically. Appearance of α and γ hydrogens in ethylene-1-hexene copolymer confirms the presence of branches in polyethylene backbone.     

Effects of thermal history,crystallinity, and solvent on the transitions and relaxations in poly(bisphenol-A carbonate)

The following system of nomenclature for the transitions and relaxations in polycarbonate has been proposed: α = T_g = 150, β = 70, γ = ?100, and δ = ?220°C (frequency range of 10–50 Hz). The three component peaks of the γ relaxation are denoted by γ₁, γ₂, and γ₃ relaxations correspond to phenylene, coupled phenylene-carbonate, and carbonate motions, respectively. Dynamic mechanical analysis of poly(bisphenol-A carbonate) using the DuPont 981–990 DMA system shows that the magnitude of the β relaxation depends upon the thermal history of the polycarbonate; annealing greatly reduces the intensity of the β relaxation. A relaxation map constructed for the β relaxation gives an activation energy of 46 kcal/mol. Exposure of polycarbonate to methylene chloride vapor for various times shows that after an induction period of about 5 min the intensity of the γ₃ relaxation at ?78°C decreases whereas the intensity of the γ₁ relaxation of ?30°C is unaffected and the ratio E″(γ₁)/E″(γ₃) increases linearly with the square root of time. This has been ascribed to the interaction of methylene chloride on the carbonate group in polycarbonate. Thermal crystallization of polycarbonate does not affect the positions of the γ relaxation and the glass transition peaks, but merely reduces their intensity. The glass transition peak intensity falls off sharply in comparison to the γ relaxation intensity. Both the γ₃ and γ₁ peaks in polycarbonate have been observed simultaneously for the first time by dynamic mechanical analysis. Impact strength measurements show that methylene chloride treatment of polycarbonate results in a change in mode of failure from ductile to brittle with a resultant 40-fold reduction in impact energy for fracture. Thermally crystallized polycarbonate exhibits brittle fracture with very low force and energy at break.     

The effect of pressure on the volume and the dielectric relaxation of linear polyethylene

The effects of pressure on the α (ca. 70°C, 1 kHz) and γ (ca. ?100°C, 1 kHz) relaxations of linear polyethylene were studied dielectrically between 0 and 4 kbar. Equation of state (PVT) data were also determined in the range of interest of these relaxations. The sample was rendered dielectrically active through oxidation (0.8 C?0 per 1000 CH₂). The α process (which occurs in the crystalline fraction) could be studied over a much wider temperature range than heretofore possible due to the effect of pressure in increasing the melting point. Examination of relaxation strength from 50 to 150°C showed that there must be two crystalline relaxation processes: the well-known α relaxation plus a competing one. The α relaxation is believed to be due to a chain twist–rotation–translation mechanism that results in rotation–translation of an entire chain in the crystal. The relaxation strength of the α process decreases and therefore indicates the presence of a second (faster and not directly observed) process that increases in intensity with increasing temperature. It is postulated that the second process is due to motion of defects that become more numerous through thermal injection at higher temperatures. Analysis of the relaxation data along with the PVT data allowed the constant volume activation energy for the α relaxation to be determined. It was found to be 19.4 ± 0.5 kcal/mole. The constant volume activation energy is important in modeling calculations of the crystal motions and is significantly smaller than the atmospheric constant pressure activation energy of 24.9 kcal/mole. The effect of pressure on the activation parameters and shape of the γ process was also determined. There has been controversy over whether the γ process occurs only in the amorphous fraction or in both the amorphous and crystalline phases. Since the two phases have quite different compressibilities, increasing the pressure should change the shape of the loss curves (versus frequency and temperature) if the process occurs in both phases. The shape (but not location) of the loss curves was found to be remarkably independent of pressure. This finding strengthens the view that the γ process is entirely amorphous in origin.     

Phase transition and paracrystalline order in solution-crystallized solid n-paraffins

Solution-crystallized single crystals of various paraffins were investigated at room temperature by nuclear magnetic resonance and by small-angle and wide-angle x-ray scattering. The samples were crystallized from various solvents and annealed 2, 5, 6, and 12°C below the melting point. The NMR spectra are separated into three components (α, β₁ and γ) of different chain-segment mobility. On combining these results with x-ray measurements and with results on polyethylene, enough information is obtained to propose a model of the paracrystalline superlattice built up by at least 30 paraffin lamellae and to find where the chains of various conformation are located in the structure. The phase transition of C₄₄H₉₀ in the solid state gives further hints for this allocation. For instance, the β₁ component of intermediate mobility increases anomalously from 3% before to 10% after the phase transition. The paracrystalline g value of the macrolattice of the orthorhombic phase is 1.5% and the gap between the lamellae is 2.2 Å. At the beginning of the phase transition, the chains incline stepwise to the lamella surface retaining the orthorhombic macrolattice distance P₀ = 58 A and enlarging the gap to 8.8 Å without changing the g value of 1.5%. The growing monoclinic phase, on the other hand, has a constant g value of 3.5% from the beginning with P_m = 52 Å and has gaps of only 3 Å between adjacent lamellae. This explains the large β₁ (ca. 10%) of these two new phases, because the mobile chain ends consist of approxiamately 1 CH₃ and 1 CH₂ group on the average. The γ component of highest micro-Brownian mobility corresponds to the γ component in polyethylene with a line width of ca. 0.07 gauss. Unlike the case of polyethylene it is produced by only a small amount (0.02–0.13) of free CH₃ groups per chain. Another fraction of the CH₃ groups belongs to the rigid component α of the crystalline phase. They are located where adjacent lamellae touch each other in crystalline-like order. Because of these contacts, stacks of lamellae about 1000 Å thick scatter coherently, and the long period P_o of the orthorhombic phase remains undestroyed by annealing until the monoclinic domains collapse to the smaller period P_m of the monoclinic phase.     

Structural differences between two crystal modifications of poly(γ-benzyl L-glutamate)

X-ray diffraction patterns were obtained for as-cast and oriented films of poly(γ-benzyl L -glutamate) and a comparison was made of the molecular packing of the α-helices in forms B and C. Form B snowed Bragg reflections on the layer lines as well as on the equator. The spacings were explained by a monoclinic unit cell comprising two chains, with a = 29.0₆ Å, b = 13 2₀ Å, c = 27.2₇ Å α = γ = 90°. and β = 96°. The chains contained in this unit cell and consequently alternating in the crystal have opposite chain directions. Form C showed continuous scattering on the layer lines and reflections on the equator. This form, therefore, is a nematiclike paracrystal in which the packing of α-helices is periodic in the direction lateral to the chain axis (a = 14.8–115.2 Å, b = 14.3–14.8 Å, c = 27 Å, and γ = 118°–120°), but the relative levels of the chains along the chain axes are displaced. The formation of form C may be attributed to random placement of two chains with mutually opposite chain directions.     

Relaxations of thermosets. III. Sub-Tg dielectric relaxations of bisphenol-A–based epoxide cured with different cross-linking agents

The sub-T_g relaxations of bisphenol-A–based thermosets cured with diaminodiphenyl methane and diaminodiphenyl sulfone have been studied by dielectric measurements over the frequency range 12 Hz to 200 kHz from their ungelled or “least” cured states to their fully cured states. Both thermosets show two relaxation processes, γ and β, as the temperature is increased toward their T_gs. In the ungelled states, the γ process is more prominent than the β process. As curing proceeds, the strength of the γ process decreases and reaches a limiting value, while that of the β process initially increases, reaches a maximum value, and then decreases. An increase in the chain iength and the number of crosslinks increases the number of -OH dipoles and/or degree of their motions in local regions of the network matrix. This is partly caused by the decreasing efficiency of segmental packing as the curing proceeds. The sub-T_g relaxations become increasingly more, separated from the α relaxation during curing. Physical aging causes a decrease in the strength of the β relaxation of the thermosets as a result of the collapse of loosely packed regions of low cross-linking density, and this decrease competes against an increase caused by further crosslinking during the “post-cure” process.     

Phase equilibria at 1375 K in three-component system of nickel-chromium-tantalum

The isothermal section of the phase equilibria diagram of the Ni-Cr-Ta system has been constructed at 1375 K by means of the method of equilibrium alloys and existence of six three-phase equilibria has been established, including γ-Ni + β-Cr + α; β-Cr + α + γ; α + γ + Ni₂Ta; γ + Ni₂Ta + μ; μ + γ + NiTa₂ and γ + NiTa₂ + β-Ta. It is shown that both cubic and hexagonal modifications are indicated in Laves binary phase.     

Crystal Structures and Characterizations of Bis(pyrrolidinedithiocarbamato)Cu（Ⅱ） and Zn(Ⅱ） Complexes

The structures of [Cu (S₂CN (CH₂)₄)₂] (1) and [Zn₂(S₂CN‐(CH₂)₄)₄] (2) have been determined by X‐ray crystallography analysis. They are all isomorphous and triclinic, space group of P1^?, with Z = 1. The lattice parameters of compound 1 is: a = 0.63483(2) nm, b = 0.74972(3) nm, c=0.78390(1) mn, α = 75.912(2)°, β = 78.634(2)° and γ = 86.845(2)°; compound 2: a = 0.78707(6) nm, b=0.79823(6) nm, c = 1.23246(9) nm, α = 74.813(2)°, β = 73.048(2)° and γ = 88.036(2)°. The copper atom is located on a crystallographic inversion center and zinc atom lies across centers of symmetry. The Cu(II) ion has a square‐planar geometry while Zn(II) has a distorted tetrahedral geometry. The thermal gravity (TG) data indicate that no structural transitions in the two compounds were abserved and the decomposition products can adsorb gas. Also they all have a high thermal stability.     

Mechanical loss processes in polysaccharides

Dynamic mechanical properties of cellophane, amylose, and dextran have been obtained over the temperature range 100–520°K and frequency range 10^?2 to 10⁺² Hz on specimens containing various amounts of water. Four mechanical transitions have been characterized. At about 180°K, there is a γ transition that has been assigned to rotation of methylol groups; no comparable transition was found to exist in dextran. At about 240°K, there is a β transition that has been assigned to rotation of methylol–water complexes, but the β transition in dextran appears to be due to some other kind of motion. In cellophane at about 450°K there is an α₂ transition which appears to have contributions from motion of chain segments in disordered regions. The α₁ transition for cellophane occurs at temperatures too high to measure and may be due to segmental motions in chains within crystalline regions. Dextran and amylose were found to have at these same temperatures α loss processes that probably correspond to glass–rubber transitions in amorphous material. The changes in these mechanical loss mechanisms due to moisture uptake suggest that sorbed water associates with glucose repeat units in ways ranging from those which stiffen molecular structure to those which allow greater freedom for other types of motion to occur.