Time-resolved small-angle neutron scattering study of polyethylene crystallization from solution

With time-resolved small-angle neutron scattering (TR-SANS), the crystallization kinetics of polyethylene from deuterated o-xylene solutions upon a temperature jump have been investigated. On the basis of a morphological model of coexisting lamellar stacks and coil chains in solution, experimental data have been quantitatively analyzed to provide structural information, such as the lamellar long period, the lamellar crystal thickness, the thickness of the amorphous layers between lamellae, the degree of crystallinity, and the crystal growth rate at various degrees of undercooling. The viability of TR-SANS for studying polymer crystallization is demonstrated through the consistency of these measurements and well-established knowledge of polyethylene crystallization from xylene solutions. One unique feature of this experimentation is that both the growth of lamellar crystals and the condensation of coil chains from solution are monitored simultaneously. The ratio of the crystal growth to the chain consumption rate decreases rapidly with a decreasing degree of undercooling. The Avrami analysis suggests that the growth mechanism approaches two-dimensional behavior at higher temperatures, and this is consistent with the observation of an increasing ratio of the sharp-surface area to the bulk crystal growth rate with temperature. The limitations, possible remedies, and potentials of TR-SANS for studying polymer crystallization are discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3133–3147, 2004     

Association of polybutadiene living anions in cyclohexane

Simultaneous measurements of static and dynamic light scattering were made for cyclohexane solutions of living polybutadiene (PB) anion to characterize PB components existing in the solutions. There were two relaxation modes in the relaxation time spectra obtained by dynamic light scattering. The static structure factor and hydrodynamic radius of the major fast relaxation component obtained are explained by the unimer‐tetramer equilibrium model. The same model is also consistent with the data of the propagation reaction rate of the PB living anion in cyclohexane. The slow relaxation component is only minor (less than 1 wt %), but has a large radius of gyration of ca. 200 nm, and is assigned to aggregates consisting of a huge number of PB living anion chains. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1401–1407, 2005     

Melt rheology of polypropylene containing small amounts of high molecular weight chain. I. Shear flow

Large enhancements of the melt strength of polypropylene (PP) were achieved by the introduction of high molecular weight polyethylene (PE) into PP. The viscoelastic properties of the high‐melt‐strength PP melts under shear flow were investigated. It was found that the rheological properties of the high‐melt‐strength PP were distinctly different from those of conventional PP. The elastic response at low frequencies was significantly enhanced in comparison with the conventional PP, implying a presence of a long relaxation time mode that was not revealed in conventional PP. In step‐shear measurements, the fast and slow relaxation processes that characterized the linear viscoelastic properties were observed also for nonlinear relaxation moduli. The dependence of the damping for the slow process of the high‐melt‐strength PP on shear strain was much weaker than that of the fast process. These rheological behaviors characterizing the long relaxation time mode were further enhanced with the increasing concentration of high molecular mass PE. The unusual shear rheological behaviors were discussed in view of the role of high molecular weight PE as a long relaxation time mode within PP. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2692–2704, 2001     

Mathematical modeling of crystallization analysis fractionation (Crystaf) of polyethylene

Four polyethylene samples (PE) with different molecular weight distributions (MWD) were analyzed by crystallization analysis fractionation (Crystaf) at several cooling rates to investigate the effect of MWD and cooling rate on their Crystaf profiles. Using these results, we developed a mathematical model for Crystaf that considers crystallization kinetic effects, which are ignored in all previous Crystaf models. The Crystaf model we proposed can fit the experimental Crystaf profiles of the 4 polyethylene resins very well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2749–2759, 2006     

Tube dilation process in star‐branched cis‐polyisoprenes

In current tube models for entanglement, the tube representing the topological constraint is considered to move with time. This tube motion results in the constraint release (CR) as well as the dynamic tube dilation (DTD), and an importance of DTD has been argued for entangled star chains. Under these backgrounds, this article examines the validity of the DTD molecular picture for the star chains. For monodisperse star chains having noninverted type‐A (parallel) dipoles in respective arms, the normalized viscoelastic and dielectric relaxation functions μ(t) and Φ(t) were found to obey a relationship μ(t) ≅ [Φ(t)]² if the tube actually dilates in the time scale of the star relaxation. For 6‐arm star cis‐polyisoprene (PI) chains (having those type‐A dipoles), dielectric and viscoelastic measurements were conducted to test this DTD relationship. Both viscoelastic and dielectric properties exhibited characteristic behavior expected from DTD models (assuming the arm retraction in the dilating tube), the exponential increase of the relaxation time and broadening of the relaxation mode distribution with increasing arm molecular weight M_a. However, in the range of M_a examined, M_a ≤ 8M_e (M_e = entanglement spacing), the above DTD relationship was not valid for a dominant part of the slow relaxation (and the models failed in this sense). Thus, for star chains at least in this range of M_a, the simple DTD picture assuming very rapid CR motion (rapid equilibration in the dilated tube) did not explain the slow relaxation behavior of star chains. This result in turn suggested the importance of the CR motion in this behavior. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1024–1036, 2000     

Effect of Molecular Weight on Enthalpy Relaxation in Syndiotactic Poly(Methyl-Methacrylate)

The structural relaxation behaviour of narrow fractions (M_w/M_n < 1.1) of syndiotactic poly(methyl methacrylate) with molecular masses ranging from 2,000 to 200,000 Daltons have been studied by DSC with two classical procedures, namely: the rate of cooling and the isothermal approaches. The apparent activation energy (Δh*) of enthalpy relaxation was evaluated from the dependence of the glass transition temperature on the cooling rate while a comparison of the apparent relaxation rates was appraised from the enthalpy loss by annealing the different samples at the same level of undercooling (T_a = T_g − 10 °C). As expected, the increase of molecular weights gives rise to both a continuous increase of Δh* and a decrease of the apparent isothermal relaxation rate. More interestingly, both Δh* and the apparent isothermal relaxation rate showed abrupt changes around the syndiotactic PMMA entanglement mass (M_e ).     

Crystal growth rate in ultrathin films of poly(ethylene oxide)

Many dynamical properties of polymers, including segmental relaxation and chain diffusion, exhibit anomalies in thin‐film samples. We extend the studies of thin‐film dynamics to the case of semicrystalline polymers and present a study of the crystal growth rate for thin films of poly(ethylene oxide). We used optical microscopy and quartz crystal microbalance techniques to characterize the kinetics of crystallization for films with thicknesses from 40 to 1000 nm for a range of temperatures near the melting point. A remarkable slowing down of the crystal growth is observed at all temperatures studied for films with a thickness of less than ～100 nm. The results can be used to suggest reductions of the mobility of chains at the crystal/amorphous interface. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2615–2621, 2001     

A COMPARATIVE STUDY OF CHAIN DYNAMICS OF DI-AND TRI-BLOCK COPOLYMERS IN SEMIDILUTE SOLUTION IN A NON-SELECTIVE SOLVENT

The chain dynamics of a pair of diblock poly(styrene-b-butadiene) (PS210-b-PB960) and triblock poly(styrene-b-butadiene-b-styrene) (PS200-b-PB1815-b-PS200) copolymers in both dilute and semidilute toluene solutions has been comparatively studied by dynamic laser light scattering. As expected, the mutual diffusion of individual chain changes into a fast cooperative diffusion of the chain segments (“blobs“) between two neighboring entanglement points for both the copolymers as the solution changes from dilute to semidilute. Further increases of the concentration lead to a second slow relaxation mode. For the triblock chains, there exists an additional middle relaxation between the fast and the slow modes.with 0.33 ＜α＜ 0.44, much smaller than 0.75 predicted or 0.72 observed for linear homopolymer chains in good solvent. It implies that the solvent quality of toluene for PB might not be as good as that for PS. Due to such a difference in solubility, it is reasonable to speculate that the PB and PS blocks are transiently segregated in semidilute solution. The relaxation of these transient PB and PS richer domains leads to the observed slow relaxation. Such a speculation is supported by the appearance of an additional slow relaxation mode in the study of polyisoprene-b-polystyrene-b-polyisoprene in semidilute solution in cyclohexane, a non-selective solvent, in which we alternated the solubility difference by a variation of the solution temperature.     

Crystallization of helical oligomers with chirality selection. I. A molecular dynamics simulation for bare helix

Helical polymers often exhibit pronounced chirality recognition during crystallization. By molecular dynamics simulation, we have already shown that the helical polymers crystallize with or without marked chirality selection depending on structural details of the polymer molecules. We have there classified the helical polymers into two categories: the bare helices made of only backbone atoms which show rather tolerant chirality selection, and the general helices with large side groups showing strict chirality recognition. Polymer crystallization is in general largely hampered and retarded by slow dynamics of the entangled chains, and therefore short helical oligomers are very suitable models for studying the chiral crystallization. We here report on molecular simulations of crystallization in the bare helical oligomer molecules by the use of Monte Carlo and molecular dynamics simulations. First we confirm the low temperature chiral crystal phase and the reversible order-disorder transition. We also observe frequent inversions of the helical sense, and the helix reversal defects propagating along the chains. Then we investigate crystallization from the melt into the chiral crystal phase. We find that the crystallization rate depends very sensitively on the degree of undercooling. The crystallization is found to be the first order transition that conforms well to the traditional picture of crystal growth in small molecules. Even when the crystallization directly into the chiral crystal phase is conducted, marked chirality selections are not observed at the early stage of crystallization; the chains adhere to the crystal surfaces selecting their helical senses rather at random resulting in racemic crystallites. The isothermal crystallization for a sufficiently long time, however, yields lamellar crystals composed of well-developed chiral domains, the growth of which seems to be accomplished through the transition back into the ordered chiral crystal phase.     

Chain contraction and nonlinear stress damping in primitive chain network simulations

Doi and Edwards (DE) proposed that the relaxation of entangled linear polymers under large deformation occurs in two steps: the fast chain contraction (via the longitudinal Rouse mode of the chain backbone) and the slow orientational relaxation (due to reptation). The DE model assumes these relaxation processes to be independent and decoupled. However, this decoupling is invalid for a generalized convective constraint release (CCR) mechanism that releases the entanglement on every occasion of the contraction of surrounding chains. Indeed, the decoupling does not occur in the sliplink models where the entanglement is represented by the binary interaction (hooking) of chains. Thus, we conducted primitive chain network simulations based on a multichain sliplink model to investigate the chain contraction under step shear. The simulation quantitatively reproduced experimental features of the nonlinear relaxation modulus G(t,γ). Namely, G(t,γ) was cast in the time-strain separable form, G(t,γ)=h(γ)G(t) with h(γ)=damping function and G(t)=linear modulus, but this rigorous separability was valid only at times t comparable to the terminal relaxation time, although a deviation from this form was rather small (within ±10%) at t>τ(R) (longest Rouse relaxation time). A molecular origin of this delicate failure of time-strain separability at t～τ(R) was examined for the chain contour length, subchain length, and subchain stretch. These quantities were found to relax in three steps, the fast, intermediate, and terminal steps, governed by the local force balance between the subchains, the longitudinal Rouse relaxation, and the reptation, respectively. The contributions of the terminal reptative mode to the chain length relaxation as well as the subchain length/stretch relaxation, not considered in the original DE model, emerged because the sliplinks (entanglement) were removed via the generalized CCR mechanism explained above and the reformation of the sliplinks was slow at around the chain center compared to the more rapidly fluctuating chain end. The number of monomers in the subchain were kept larger at the chain center than at the chain end because of the slow entanglement reformation at the center, thereby reducing the tension of the stretched subchain at the chain center compared to the DE prediction. This reduction of the tension at the chain center prevented completion of the length equilibration of subchains at t～τ(R) (which contradicts to the DE prediction), and it forces the equilibration to complete through the reptative mode at t?τ(R). The delicate failure of time-strain separability seen for G(t,γ) at t～τ(R) reflects this retarded length equilibration.     

Effect of chain entanglements on plastic deformation behavior of ultra‐high molecular weight polyethylene

Samples of ultra‐high molecular weight polyethylene, in which the chain topology within the amorphous component was altered using two‐stage processing, including crystallization at high pressure in the first step, were produced and their deformation behavior in the plane‐strain compression was studied. Deformation and recovery experiments demonstrated that the state of the molecular network governed by entanglement density is one of the primary parameters controlling the response of the material on the imposed strain, especially at moderate and high strains. Any change in the concentration of entanglements markedly influences the shape of the true stress–true strain curve. The strain hardening modulus decreases while the onset of strain hardening increases with a decrease of the entanglement density within the amorphous component. Density of entanglements also influences the amount of rubber‐like recoverable deformation and permanent plastic flow. In material of the reduced concentration of entanglements permanent flow appears easier and sets in earlier than in the material with a higher entanglement density, becoming a favorable deformation mechanism at moderate strains. As a result, strong strain hardening is postponed to higher strain when compared with the samples of equilibrium entanglement density. In the samples of an increased entanglement density the molecular network becomes stiffer, with a reduced ability of strain induced disentangling of chains. Consequently, there is a less permanent flow and strain hardening begins earlier than in the reference material of an unaltered chain topology. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 276–285, 2010     

Dislocation approach to the plastic deformation of semicrystalline polymers: Kinetic aspects for polyethylene and polypropylene*

The plasticity of semicrystalline polymers is analyzed in the framework of Young's dislocation model under the assumption of nucleation of screw dislocations from the lateral surface of the crystalline lamellae. It is proposed that the driving force for the nucleation and propagation across the crystal width of these screw dislocations relies on chain twist defects that migrate along the chains stems and allow a step‐by‐step translation of the stems through the crystal thickness. Such defects are identified as thermally activated conformational defects responsible for the so‐called crystalline relaxation. Dislocation kinetic equations are derived. Plastic flow rates attainable by dislocation motion in polyethylene and polypropylene are assessed with frequency–temperature data of the crystalline relaxation. Comparisons are made with experimental strain rates that enable homogeneous plastic deformation. In addition to temperature, the crystal lamellar thickness, which is a basic factor of the plastic flow stress in Young's dislocation model, is a major factor in dislocation kinetics through its influence on chain twist activation. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 593–601, 2002; DOI 10.1002/polb.10118     

Tear anisotropy in films blown from polyethylenes of different macromolecular architectures

Blown films of different types of polyethylenes, such as branched low‐density polyethylene (LDPE) and linear high‐density polyethylene (HDPE), are well known to tear easily along particular directions: along the film bubble's transverse direction for LDPE and along the machine direction (MD) for HDPE. Depending on the resin characteristics and processing conditions, different structures can form within the film; it is therefore difficult to separate the effects of the crystal structure and orientation on the film tear behavior from the effects of the macromolecular architecture, such as the molecular weight distribution and long‐chain branching. Here we examine LDPE, HDPE, and linear low‐density polyethylene (LLDPE) blown films with similar crystal orientations, as verified by through‐film X‐ray scattering measurements. With these common orientations, LDPE and HDPE films still follow the usual preferred tear directions, whereas LLDPE tears isotropically despite an oriented crystal structure. These differences are attributed to the number densities of the tie molecules, especially along MD, which are considerably greater for linear‐architecture polymers with a substantial fraction of long chains, capable of significant extension in flow. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 413–420, 2005     

Mechanical properties of high‐density polyethylene and crosslinked high‐density polyethylene in crude oil and its components

The tensile and stress‐relaxation properties of an uncrosslinked and a loosely silane‐crosslinked high‐density polyethylene exposed to organic “crude‐oil” penetrants were assessed. The measurements were performed on penetrant‐saturated samples, surrounded by the organic liquid throughout the experiment. The penetrant solubilities in the two polymers were similar and in accordance with predicted values based on the solubility parameter method. The stiffness and strength of the swollen samples were significantly less than those of the dry samples, indicating a plasticization of the amorphous component. Raman spectroscopy on polyethylene exposed to deuterated n‐hexane revealed a penetrant‐induced partial melting/dissolution of the crystal surface and an intact crystal core component. The stress‐relaxation rates, within the time frame of the experiment (～1 s to 18 h), were approximately the same, independent of silane‐crosslinks and the presence of penetrants. This indicated that the mechanical α‐relaxation, which is the main relaxation process occurring in the measured time interval, was not affected by the penetrants. Consequently, its rate seemed to be independent of the crystal surface dissolution (decrease in the content of crystal‐core interface). The shape of the “log stress–log time” curves of the swollen samples was, however, different from that of the dry samples. This was most likely attributed to a time‐dependent saturation of penetrant to a higher level associated with the stretched state of the polymer sample. The silane crosslinks affected only the elongation at break, which was less than that of the uncrosslinked material. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 641–648, 2006     

Dynamics of polyethylene melts studied by Monte Carlo simulations on a high coordination lattice

A detailed comparison is made between the experiment, prior simulations by other groups, and our simulation based on a newly designed dynamic Monte Carlo algorithm, on the dynamics of polyethylene (PE) melts. The new algorithm, namely, noncross random two-bead move has been developed on a high coordination lattice (the 2nnd lattice) for studying the dynamics of realistic polymers. The chain length (molecular weight) in our simulation ranges from C40 (562 Da) to C324 (4538 Da). The effects of finite chain length have been confirmed and significant non-Gaussian statistics evidently results in nonstandard static and dynamic properties of short PE chains. The diffusion coefficients scale with molecular weight (M) to the −1.7 power for short chains and −2.2 for longer chains, which coincides very well with experimental results. No pure Rouse scaling in diffusion has been observed. The transitional molecular weight to the entanglement regime is around 1500 Da. The detailed mean square displacements of middle bead (g1) are presented for several chain lengths. The reptation-like slowdown can be clearly observed only above M ∼ 2400 Da. The slope 0.25 predicted by the theory for the intermediate regime is missing; instead a slope close to 0.4 appears, indicating that additional relaxation mechanism exists in this transitional region. The relaxation times extracted by fitting the autocorrelation function of end-to-end vectors with reptation model scale with M to 2.5 for long chains, which seemingly conflicts with the scaling of diffusion. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2556–2571, 2006     

Relaxation processes in semidilute solutions of polymers in liquid crystal solvents

We investigate the relaxation phenomena in a polymer (polystyrene)/liquid crystal (4-cyano-4'-n-octyl-biphenyl) system, in its homogeneous isotropic phase near the isotropic-isotropic, isotropic-nematic, and isotropic-smectic coexistence curve, using both polarized and depolarized photon correlation spectroscopy (PCS). We study this system for different polystyrene molecular weights (4750, 12 500, and 65 000 g/mol), different compositions (50, 40, 30, and 10% polystyrene (PS) by weight), and different temperatures close to phase boundaries. First of all, we determine the phase diagrams of this system for the different molecular weights. The shape of the phase diagrams strongly depends on the molecular weight. However, in all cases, at low temperatures, these systems separate into an almost pure liquid crystalline (LC) phase and polystyrene-rich phase. PCS measurements show that the relaxation processes in the homogeneous phase are not affected by the proximity of the nematic, or smectic, boundaries (even at a temperature of 0.1 degrees C above the phase separation in two phases). In polarized PCS experiments, we always see three relaxation processes well separated in time: one, very fast, with a relaxation time of the order of 10(-5) s; a second one with a relaxation time within the range 10(-2)-10(-3) s; and a last one, very slow, with a relaxation time of the order of 1 s. Both the fast and slow modes are independent of the wave vector magnitude, while the intermediate relaxation process is diffusive. In depolarized PCS experiments, the intermediate mode disappears and only the fast and slow relaxation processes remain, and they are independent of the magnitude of the wave vector. The diffusive mode is the classical diffusive mode, which is associated with the diffusion of polymer chains in all polymer solutions. The fast mode is due to the rotational diffusion of 4-cyano-4'-n-octyl-biphenyl (8CB) molecules close to polystyrene chains (transient network). Finally, we assign the slowest mode to reorientational processes of small aggregates of PS chains that are not dissolved in 8CB.     

Molecular orientation behavior of poly(vinyl chloride) as influenced by the nanoparticles and plasticizer during uniaxial film stretching in the rubbery stage

The structural evolution during uniaxial stretching of poly(vinyl chloride) films was studied using our real time spectral birefringence stretching machine. The effect of clay loading and the amount of plasticizer as well as the rate effects on the birefringence development and true mechanical response are presented with a final model summarizing the molecular phenomena during stretching. Mechano‐optical studies revealed that birefringence correlated with mechanical response (stress, strain, work) nonlinearly. This was primarily attributed to the preexisting strong network of largely amorphous chains connected via small crystallites that act as physical crosslinking points. These crystallites are not easily destroyed during the high‐speed stretching process as evidenced from the birefringence–true strain curves along with the X‐ray crystallinity measurements. At high speeds, the amorphous chains do not have enough time to relax and hence attain higher orientation levels. The crystallites, however, orient more efficiently when stretched at slow speeds. Apparently, some relaxation of the surrounding amorphous chains helps rotate the crystallites in the stretching direction. Overall birefringence is higher at high stretching speeds for a given true strain value. When the nanoparticles are incorporated, the orientation levels are increased significantly for both the crystalline and amorphous phases. Nanoplatelets increase the continuity of the network because they have strong interaction with the amorphous chains and/or crystallites. This in turn helps transfer the local stresses to the attached chains and increase the orientation levels of the chains. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 724–742, 2005     

Structure,conformation and dynamics of polymer chains at solid melt interfaces

We have performed molecular dynamics, and lattice Monte Carlo simulations of polymeric melts in the vicinity of solid surfaces. The structural features of the solid-melt interface were very simple. The interfacial width was comparable to the segment size. Inside this narrow interface the segment density profile was oscillatory. The density oscillations were much less pronounced than those present at solid-atomic liquid interfaces. On a scale much larger than the segment size, chain conformations were found to be identical with those of ideal chains next to a reflective barrier. In particular, the number of surface-segment contacts scaled like the square root of the molecular weight. Extensive molecular dynamics simulations showed that chain desorption times increase with molecular weight but at a rate much slower than the longest relaxation time of Rouse chains. Therefore, sufficiently long chains desorbed almost freely from the surface despite the presence of attractive surface-segment interactions. A study of chain relaxation dynamics confirmed that the Rouse modes constitute an appropriate set of normal coordinates for chains in the melt interacting with a solid surface. The effect of the surface on mode relaxation was significant. All relaxation processes of chains located within a couple of radii of gyration from the surface were slowed down considerably. This effect, however was approximately the same for fast and slow modes and independent of molecular weight for sufficiently long chains.     

Modeling of the linear viscoelastic behavior of low‐density polyethylene

We predict the linear viscoelastic behavior of low‐density polyethylene from both the molecular‐weight distribution and the individual structure of each species in the sample. The “structure map” of the samples was derived from SEC measurements. This map is a three‐dimensional representation of the seniority distribution, and represents the probability of existence of a segment with seniority i in a molecule of molecular weight M. Moreover, results from the kinetics of the free radical polymerization of polyethylene show that the molecular weight of the segments increases according to their seniority. Finally, tube dilatation was generalized to the case of polydisperse samples. The solvent behavior of the relaxed segments was included through a continuous function of time that describes the instantaneous state of the entanglement network in the sample. The comparison between the theoretical predictions and the experimental data shows a good agreement over the whole experimental frequency range. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43:1973–1985, 2005