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.     

Dynamic study of the noncrystalline phase of 13C-labeled polyethylene by variable-temperature 13C CP/MAS NMR spectroscopy

The ¹³C spin-lattice relaxation times T₁ of ¹³C-labeled polyethylene crystallized under different conditions were measured at temperatures from ?120 to 44°C by variable-temperature solid-state high-resolution ¹³C nuclear magnetic resonance (NMR) spectroscopy, in order to determine accurately the dynamics of the noncrystalline region of the polymer. From these results, it was found that the T₁ minimum for the CH₂ carbons in the noncrystalline region of solution-crystallized polyethylene with high crystallinity appears at higher temperature by about 20°C than that of melt-quenched polyethylene with low crystallinity. This means that the molecular motion of the CH₂ carbons in the noncrystalline regions is more constrained at a given temperature in the material of higher crystallinity. Furthermore, dynamics of the noncrystalline region is discussed in terms of the ¹³C dipolar dephasing times.     

Spin lattice relaxation in linear polyethylene

The proton spin-lattice relaxation times (T₁) of linear polyethylenes (PE) of varying morphology were measured as a function of temperature. The T₁ of oriented bulkcrystallized and solution-crystallized material was isotropic, in disagreement with calculations based on a sample dipole pair model. Motion in the non-crystalline regions of the samples is shown to be responsible for the T₁ minimum occurring around ?20°C. The dependence of T₁ at the minimum on the long period reinforces the model of an amorphous fraction composed of disordered lamellar surface layers. The temperature of the T₁ minimum and the dependence of T₁ on the long period imply that the mobility of these amorphous regions is reduced in cold-drawn and solution-crystallized samples. This mobility irreversibly increases with annealing. In highly relaxed samples the motion of a small portion of the disordered regions is almost liquidlike, as indicated by the presence of a second shorter T₁.     

NMR relaxation study of crosslinked cis-1,4-polybutadiene

Proton relaxation measurements have been used to investigate the effects of crosslinking on the segmental motion in cis-1,4-polybutadiene samples. The temperature dependence of proton spin–lattice relaxation time T₁ and spin–spin relaxation time T₂ at 60 and 24.3 MHz are reported in cis-1,4-polybutadiene (PB) samples with different crosslink density including uncrosslinked PB and samples with 140, 40, and 14 repeat units between crosslinks. In addition, spin-lattice relaxation times in rotating coordinate frame, T_1p, have also been determined. The relaxation data are interpreted in terms of the effects of crosslinks on segmental chain motions. Because of their sensitivity to low-frequency motion, T₂ data are of major interest. At temperatures well above the T₁ minimum the small T₂ temperature dependence resembles solidlike behavior reflecting the nonzero averaging of dipolar interactions due to anisotropic motion of the chain segments between crosslinks. The magnitude of T₂ at 60°C is found to be proportional to the average mass between crosslinks.     

Dielectric properties of complex zn(II) salts of ethylene-methacrylic acid copolymer with n-hexylamine

This article describes dielectric properties of complex Zn(II) salts of ethylene-methacrylic acid copolymer (5.4 mol% methacrylic acid) with n-hexylamine. In all samples, the β′ relaxation near 340 K and γ relaxation near 170 K are observed. These are assigned, respectively, to micro-Brownian molecular motion of long segments above T_g and to local molecular motion of short segments below T_g. The dielectric results indicate that ionic clusters are not formed in these systems.     

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.     

A dielectric study of molecular relaxation in oxidized and chlorinated polyethylenes

A study was made of the dielectric relaxation in polyethylenes rendered dielectrically active through oxidation (0.5–1.7 carbonyls/1000 CH₂) and chlorination (14–22 Cl/1000 CH₂). Both linear and branched polymers were studied. All of the relaxations between the melt and ?196° were studied in the frequency range 10 Hz to 10kHz (100 kHz in the chlorinated samples). In the linear samples a wide range of crystallinities was studied (55% in quenched specimens to 95% in extended-chain specimens obtained by crystallization at 5 kbar). As is consistent with its being a crystalline process, the α peak was found to discontinously disappear on melting of the samples and reappear on recrystallizing on cooling. The disappearance of the smaller crystals before the larger ones appeared to be evident in the isothermal loss versus frequency curves. The relaxation strength of the α process increases with crystallinity. The measured relaxation strength is less than that expected on the basis of direct proportionality to the crystalline fraction with full contribution of all dipoles in the crystalline material. However, the intensity is not sufficiently low for the process to be interpreted in terms of reorientation of localized conformational defects in the crystal. The variation of intensity with crystallinity is best interpreted in terms of full participation of crystalline dipoles but with selective partitioning of both carbonyls and chlorines favoring the amorphous domains. A strong correlation of the α loss peak location (T_max at constant frequency or log f_max at constant T) with crystallinity for both carbonyl and chlorine containing polymers was found. This variation is interpreted in terms of chain rotations in the crystal where the activation free energy depends on crystal thickness. The dependence of log f_max and T_max on lamellar thickness as well as a comparison with the loss peaks of ketones dissolved in parafins indicates that the chain rotation is not rigid and is accompanied by twisting as the rotation propagates through the crystal. In agreement with previous studies the β process is found to be strong only in the branched polymers but can be detected in the chlorinated linear polymer. The β process was resolved from the α in the branched samples by curve fitting and its activation parameters determined. The γ relaxation peak in oxidized polymers including its high asymmetry (low-temperature tail) and increasing ε_max with increasing frequency and temperature when plotted isochronally can be interpreted in terms of a simple nearly symmetrical relaxation time spectrum that narrows with increasing temperature. No increase in relaxation strength with temperature was found. The chlorinated polymers behave similarly but appear to have some Boltzmann enhancement (450–750 cal/mole) of relaxation strength with temperature. The dependence of relaxation strength on crystallinity indicates that the process is an amorphous one. Further, no evidence of relaxation peak shape changes with crystallinity that could be interpreted in terms of a crystalline component in addition to the amorphous one was found. The comparison of the γ relaxation strength with that expected on the basis of full participation of amorphous dipoles indicates that only a small fraction (～10% in oxidized linear polymers) of them are involved in the relaxation. Thus it would seem that a glass–rubber transition interpretation is not indicated but rather a localized chain motion. It is suggested that the γ process, including its intensity, width, and activation parameters, can be interpreted in terms of an (unspecified) localized conformational (bond rotation) motion that is perturbed by differing local packing environments. The thermal expansion lessens the effects of variations in packing and leads to narrowing with increasing temperature. The conformational motion itself leads to increase in thermal expansion and hence a transition in the latter property. Some previously proposed localized amorphous phase conformational motions appear to be suitable candidates for the bond rotation motion. A weak relaxation peak found at temperatures below the γ and at 10 kHz may possibly be the dielectric analog of the δ cryogenic peak found previously mechanically at lower frequencies.     

A pulsed NMR study of the effects of initial morphology on the structure of extrusion-drawn poly(ethylene terephthalate)

Proton spin–spin relaxation times and the Weibull coefficient have been measured as functions of temperature for poly(ethylene terephthalate) (PET) drawn at 50°C in both the amorphous and the semicrystalline (50%) states. Two relaxation times T_2a (long) and T_2c (short) are observed for all samples. They are ascribed, respectively, to the relaxation of the amorphous and of the crystalline components including highly strained noncrystalline segments. Effects of initial morphology are found for chain mobility in the noncrystalline regions and for the crystal perfection, evaluated from T_2a and the Weibull coefficient μ_c of the T_2c-component, respectively. For all draw ratios, T_2a for extrudates prepared from the semicrystalline polymer (C-50) is short compared to that for preparations from the amorphous (A-50) polymer. In the A-50 samples, the perfection of stress-induced crystals increase with increasing draw ratio. In the C-50 samples, the crystal orientation increases, whereas the perfection decreases with increasing draw ratio. To improve the crystal perfection, annealing at higher temperature or longer time is required for C-50 as compared with A-50. The value of μ_c correlates well with the change in crystal perfection during deformation and annealing.     

Molecular relaxation in the blends of polystyrene/poly(2,6-dimethyl-1,4-phenylene oxide) at low temperature

Molecular relaxation behavior in terms of the α, β, and γ transitions of miscible PS/PPO blends has been studied by means of DMTA and preliminary work has been carried out using DSC. From DSC and DMTA (by tan δ), the observed α relaxation (T_α or T_g) of PS, PPO, and the blends, which are intermediate between the constituents, are in good agreement with earlier reports by others. In addition, the β transition (T_β) of PS at 0.03 Hz and 1 Hz is observed at −30 and 20°C, respectively, while the γ relaxation (T_γ) is not observed at either frequency. The T_β of PPO is 30°C at 0.03 Hz and is not observed at 1 Hz, while the T_γ is −85°C at 0.03 Hz and −70°C at 1 Hz. On the other hand, blend composition-independent β or γ relaxation observed in the blends may be a consequence of the absence of intra- or intermolecular interaction between the constituents at low temperature. Thus it is suggested that at low temperature, the β relaxation of PS be influenced solely by the local motion of the phenylene ring, and that the β or γ relaxation of PPO be predominated by the local cooperative motions of several monomer units or the rotational motion of the methyl group in PPO. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1981–1986, 1998     

Pressure dependence of the β molecular relaxation process and dielectric properties of polyvinylidene fluoride

The effects of hydrostatic pressure to 20 kbar on the β molecular relaxation process of polyvinylidene fluoride (PVDF) and on the dielectric properties in the neighborhood of this relaxation have been investigated. This relaxation has a strong influence on the electrical and mechanical properties of PVDF. Pressure causes a large shift to higher temperatures (～ 10K/kbar) of the dielectric relaxation peak and a decrease in the width of the distribution of relaxation times. This slowing down of the relaxation process is discussed in terms of the Vogel–Fulcher equation and related models, and it results from an increase in both the energy barrier to dipolar motion and the reference temperature (T₀) for the kinetic relaxation process which represents the “static” dipolar freezing temperature for the process. The general applicability of the Vogel–Fulcher equation to relaxional processes in polymers and other systems is briefly discussed. The pressure dependence of the dielectric constant both above and below the relaxation peak temperature (T_max) is found to be dominated by the change in polarizability. The effect is larger above T_max because of the relatively large decrease in the dipolar orientational polarizability with pressure.     

NMR observations of drawn polymers. VII. Nylon 66 fibers

Wide-line NMR spectra have been obtained on an oriented sample of drawn nylon 66 fibers at temperatures between ?196°C and 200°C and at alignment angles between the fiber axis and the magnetic field of 0°, 45°, and 90°. At ?196°C, 20°C, and 180°C, the complete angle dependence of the NMR spectrum has been measured. The second moments of these spectra have been compared to theoretical second moments calculated for various models of chain segmental motion in an attempt to elucidate the mechanisms involved in the low-temperature segmental motion (γ process) and the high-temperature segmental motion (α_c process). In agreement with earlier suggestions, the present results indicate that the γ process consists of segmental motion in noncrystalline regions. The overall decrease in second moment caused by the γ process is consistent with a model in which all noncrystalline segments rotate around axes nearly fixed in space. Furthermore, this decrease shows a pronounced dependence on the alignment angle. It is believed that this is due to tie molecules which become highly oriented along the fiber axis during drawing; their axes of rotation will therefore be nearly parallel to the fiber axis. The segments in noncrystalline entities such as chain folds and chain ends are less well oriented along the fiber axis and make an essentially isotropic contribution to the second moment decrease. The second moment at 180°C indicates the presence of considerable motion in the crystalline regions, and this motion is denoted the α_c process. The second moment S_c of the crystalline regions is strongly dependent on the alignment angle, the predominant feature being a relatively high value of the second moment when the fiber axis is directed parallel to the magnetic field. This is in qualitative, but not quantitative, agreement with the motional model recently advanced by McMahon, which assumes full rotation of the chains around their axes. Excellent quantitative agreement with experiment has been obtained by superimposition of rotational oscillation around the chain axis of amplitude roughtly 50°, and torsion of the chains with neighboring CH₂ groups oscillating around the C? C bond with a relative amplitude of about 40°. A model in which the chains perform rotational jumps of 60° between two equilibrium sites has also been considered (60° flip-flop motion). A distinction between this model and rotational oscillation has not been possible.     

NMR observations of drawn polymers. VIII. Doubly oriented nylon 66

A wide-line NMR study of chain segmental motion in nylon 66 has been made on a rolled sheet having “double orientation.” In this sheet the crystallite c axis, i.e., the molecular chain axis, is oriented preferentially along the roll direction, and the crystallographic (010) plane lies predominantly parallel to the roll plane, or the plane of the sheet. The direction of the applied magnetic field with respect to the sheet is characterized by two angles, the polar angle γ subtended by the roll direction and the magnetic field, and an azimuthal angle ?. NMR spectra were taken at various values of the angles γ and ? and at three temperatures ?196°C, 20°C, and 180°C. The second moments of the absorption spectra taken at 180°C were compared with theoretical predictions of second moments based on two models for the high-temperature segmental motion (called the α_c process) in crystalline regions of nylon 66. One model consists of rotational oscillation with amplitudes δ of segments around their axies. The second model is denoted 60° flip-flop motion and consists of rotational 60°C jumps of the segments around their axes between two equilibrium sites with the possibility that the segments also oscillate with a general amplitudes δ around each site. The experimental results are consistent with fairly large amplitudes δ, in which case both models approach the limiting case of full segment rotation. For this reason the experiments do not allow a distinction between the two models. From the second moments at ?196°C and 20°C the decrease in second moment due to the low temperature segmental motion, the γ process, is obtained. This motion occurs in noncrystalline regions of nylon 66 and is found to cause a decrease in second moment which is strongly dependent on the two angles γ and ?, implying double orientation of the noncrystalline segments. It is suggested that at low temperatures the noncrystalline segments become immobilized in sites dictated by the crystallite orientation through the extensive hydrogen bonding known to exist in nylon 66.     

Molecular motion and relaxation studies of aliphatic polyureas by thermal windowing thermally stimulated depolarization current technique

Molecular motion and relaxation studies using a thermal windowing thermally stimulated depolarization current (TW‐TSDC) were performed for aliphatic polyureas 7 and 9. Global thermally stimulated depolarization current gave three characteristic major peaks corresponding to the α, β, and γ relaxation modes at 78.5, −44, and −136°C for polyurea 7 and at 80, −50, and −134°C for polyurea 9, respectively. The α relaxation is related to the large‐scale molecular motion due to micro‐Brownian motion of long‐range segments. This relaxation is significantly related to the glass‐transition temperature. The β relaxation is caused by the local thermal motion of long‐chain segments. The γ relaxation is caused by the limited local motion of hydrocarbon sections. Temperature dependence of relaxation times was expressed well using Vogel–Tammann–Fulcher (VTF) expression. 3‐D simulation of dielectric constants of dielectric strength and loss factor were performed in the frequency range from 10⁻⁶ to 10⁴ Hz and temperature range from −150 to 250°C, using the relaxation parameters obtained from the TW‐TSDC method. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 88–94, 2000     

High-resolution solid-state 13C NMR study of ethylcellulose films

Ethylcellulose films cast from concentrated solutions of chloroform, benzene, and carbon tetrachloride were subjected to the NMR relaxation measurements including ¹H spin-lattice relaxation time (T_1H), rotating-frame ¹H spin-lattice relaxation time (T_1ρH), and ¹³C spin-lattice relaxation time (T_1C). The values of T_1ρH for carbons in the glucose units of ethyl-cellulose were of the same order of magnitude as those reported for the crystalline and noncrystalline regions of ramie cellulose. The values of T_1C for unsubstituted C2, C3 carbons were smaller than those for the corresponding carbons in the noncrystalline region of native celluloses. The T_1C values for unsubstituted C2, C3, and substituted C6 carbons showed a small but definite dependence on the solvent from which the films were cast. © 1993 John Wiley & Sons, Inc.     

Dynamics of macromolecular chains. VI. Carbon 13 and proton nuclear magnetic relaxation of polystyrene in solution

Spin-lattice ¹H and ¹³C nuclear magnetic relaxation (NMR) times T₁ have been measured for solutions of polystyrene in hexachlorobutadiene at two different frequencies. Some nuclear Overhauser enhancements and linewidths have also been determined. At 15 and 25 MHz the relaxation times T₁ of the ortho and meta carbons show two different dependences on temperature. These measurements indicate internal motion of phenyl groups around the C_α—C_para axis. A single isotropic correlation time is inadequate to explain the relaxation data for the para carbon. Use of a diamond-lattice motional model reveals that segmental reorientation of the chain backbone of polystyrene can be described in terms of two correlation times, ρ characterizing the three-bond motion process, and θ reflecting either isotropic motions of subchains or departure from an ideal lattice. Data on low-molecular-weight polystyrene indicate the participation of overall rotatory diffusion in the relaxation process. This motion is no longer efficient in high-molecular-weight polymers, where relaxation is due to segmental reorientation.     

α‐ and β‐Relaxations in neat and antiplasticized polybutadiene

Dielectric spectroscopy was carried out to measure the α‐relaxation (local segmental motion) and the higher frequency, secondary relaxation (β‐mode) in 1,4‐polybutadiene, both neat and containing a nonpolar diluent, mineral oil. The α‐relaxation shifted to lower frequencies (antiplasticization) in the presence of the diluent, suggesting the glass temperature of the latter is higher than the T_g of the polymer (i.e., >187K). The T_g of neat mineral oil cannot be determined directly, due to crystallization. While the diluent increased the magnitude of the α‐relaxation times, it had no effect on the β‐relaxation. Moreover, neither the shape of the α‐relaxation function nor its temperature dependence was influenced by the diluent. From this we conclude that the main effect of the mineral oil was to increase the local friction, without changing the degree of intermolecular cooperativity of the molecular motions. We also find that near the glass temperature, there is rough agreement between the time scale of the secondary relaxation process and the value of a noncooperative relaxation time estimated from theory. This approximate correspondence between the two relaxation times also holds for 1,2 polybutadiene. However, the β‐process cannot be identified with the noncooperative α‐relaxation, and the relationship between them is not quantitative. © 2000 John Wiley & Sons, Inc.* J Polym Sci B: Polym Phys 38: 1841–1847, 2000     

Dynamics of junction point motions in model network polymers

³¹P solid-state exchange 2D NMR and spin-lattice relaxation times (T₁^P) have been used to investigate the motion of a crosslink unit in model networks. The networks were formed from tris(4-isocyanatophenyl) thiophosphate with telechelic poly(propylene glycol) or poly(tetrahydrofuran). From the variation of the 2D NMR pattern with temperature and mix time, the motion of the crosslink is identified as Brownian reorientational diffusion. Good simulations of the spectra were obtained using the Williams-Watts distribution of correlation times. The temperature dependence of the crosslink motion follows the WLF equation. The parameters derived from the NMR data are sufficient to describe the temperature dependence and breadth of both the dielectric and mechanical loss associated with the glass transition. The T₁^P relaxation data fitted equally well to the Cole-Cole or the Williams-Watts relaxation functions. The motion of the crosslinks can be described quantitatively by the activation energies and the coupling parameters.     

Solid‐state NMR analyses of the crystalline–noncrystalline structure and its thermal changes for ethylene ionomers

The crystalline–noncrystalline structure and its structural changes from thermal treatments for ethylene ionomers have been investigated with solid‐state ¹³C and ²³Na NMR spectroscopy. ¹³C spin–lattice relaxation time (T_1C) measurements reveal that as‐received ethylene ionomers have much enhanced molecular mobility in the crystalline region in comparison with conventional polyethylene samples. By appropriate annealing, however, polyethylene‐like morphological features reflecting T_1C behavior can also be observed. ¹³C spin–spin relaxation time (T_2C) measurements for the noncrystalline region reveal the existence of two components with different T_2C values, and these two components have been assigned to the crystalline–amorphous interfacial and rubbery–amorphous components. These results indicate that the structure of the major part of the noncrystalline region in the ethylene ionomers is similar to that of bulk‐crystallized polyethylene samples, regardless of possible ionic aggregates. The origin of the lower temperature endothermic peak in the heating process of the differential scanning calorimetry curve observed for the as‐received sample has also been examined somewhat in detail. As a result, it is proposed that the melting of smaller crystallites produced during storage at room temperature is the origin of the lower temperature peak. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1142–1153, 2002     

A.C. dielectric and TSC studies of constrained amorphous motions in flexible polymers including poly(oxymethylene) and miscible blends

Poly(OxyMethylene) (POM) and its miscible blends were studied by multifrequency A.C. dielectric and thermally stimulated currents (TSC). The blends contained small amounts of either poly(vinyl phenol), which is a high glass transition (T_g) diluent, or a styrene-co-hydroxy styrene oligomeric low T_g diluent. The variation of the 10°C “β” transition with blend composition proves that it is the glass transition, and that the −70°C “γ” transition is a local motion. Dielectrically the β transition is very weak in pure POM even in fast-quenched samples. The TSC thermal sampling method also detected two cooperative transitions, γ and β, in POM and its blends, and was used to directly resolve the γ transition into low and high activation energy components. If one considers the contribution of exclusion of the diluents from the crystal lamellae, it is shown that the blends behave like typical amorphous blends as a function of concentration. The effect of crystals on amorphous motions is examined in light of comparison with van Krevelen's³⁷ predictions of an “amorphous” T_g, and the transitions in POM are contrasted with those for other semicrystalline polymers. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2121–2132, 1997     

Dielectric relaxation phenomena in a series of polyhydroxyether copolymers of bisphenol-A—endcapped polyethylene glycol with epichlorohydrin

Dielectric relaxation spectra of a series of polyhydroxyether copolymers have been obtained. It has been shown that the systems exhibit very similar relaxation spectra with the α(T_g) process a function of molecular weight. All systems exhibit two secondary relaxations: β (ca. 240 K) and γ (ca. 180 K). These have been assigned as hydroxyl motion and main-chain motion, respectively. The peak positions are not functions of composition in the ranges studied. The effect of sorbed water on the relaxation spectra is discussed.