Plasticity of Semicrystalline Polymers

Semi-crystalline polymers can be deformed up to a very high strain. The deformation process involves frequently a complete molecular rearrangement of the chain-folded lamellar morphology into a more or less chain-unfolded fibrillar microstructure. This transformation is likely to occur through an intermediate state of high molecular disorder at a local scale. It led to the formulation of a concept of strain-induced melting-recrystallization process as a main mechanism of the structure transformation. In contrast, several structural features occurring at moderate plastic strains are relevant to strictly crystallographic processes. The plastic deformation process of semicrystalline polymers and the micromechanisms involved are discussed. A critical discussion of experimental findings is made to point out the strength or the deficiency of the various argumentations. It is demonstrated that the crystallographic slip mechanisms, including slips: transverse and along the chains are the basic deformation mechanisms in the deformation sequence, active at all strain levels. Direct microscopic evidence of chain slip activity even at well advanced stages of the deformation process is presented. In contrary, the melting-recrystallization seems to be restricted to the high-strain stage accompanied by chain unfolding and perhaps limited to only a small fraction of the crystalline phase. In addition the experimental results demonstrates clearly that the cavitation, necessary in the Peterlin's model, is really unessential in producing high deformation and appearance of the final highly oriented structure. This can be effectively accomplished with only crystallographic mechanisms employed. A very important role in the deformation sequence is played by the partially reversible shear deformation of amorphous interlamellar layers, producing not only high orientation of amorphous component but also influencing deeply the deformation of crystalline phase, since both phases are strongly connected and must deform simultaneously and consistently.     

Energetics of Stretching of Conformational Defects in Extended Poly(methylene) Chains

The deformation energetics of highly extended poly(methylene) segments with conformational defects of the kink and jog types, is investigated by molecular mechanics calculations. The deformation potential displays abrupt discontinuities as a result of sudden gauche‐to‐trans conformational transitions accompanied by a release of the elastic energy stored in all valence parameters. By stretching, the chain defects are sequentially annihilated, with the weakest elements interconverting first. Due to sudden drops in force the calculated force–length curves F(R) display a sawtooth‐like profile. The force jumps define a maximum load F_c that defect chains can bear prior to conformational “yielding”. The F_c in the range about 0.7–1.1 nN is found in highly extended multikink chains. The results suggest that the sawtooth‐like profile can be a common feature of mechanochemistry of bridging polymers with the restricted number of available conformations. A similar pattern of F(R) curves were previously observed at stretching and sequential unfolding of compact structural domains in biomacromolecules. Further, the calculations predict a distinct reduction of the longitudinal Young's modulus E with increasing concentration of kinks in molecules.     

Computer modeling of the crystallization process of single‐chain ethylene/1‐hexene copolymers from dilute solutions

Langevin molecular dynamics (LMD) simulations have been performed to understand the role of the short chain branches (SCB) on the formation of ordered domains by cooling dilute solutions of ethylene/α‐olefins copolymer models. Three different long single‐chain models (C₂₀₀₀) with 0, 5, and 10 branches each 1000 carbons were selected. These models were equilibrated at high reduced temperature (T* = 13.3) and cooling in steps of 0.45 until the final temperature (T* = 6.2) by running a total of 35 × 10⁶ LMD steps. During the cooling process, global order parameter, torsion distribution, position of the branches, and local‐bond order parameter were calculated and monitored. The peaks of crystallization for each model were calculated by differentiating the global order parameter with temperature. The T_c (crystallization temperature) decreases as the number of branches increases as has been experimentally reported. The formation of order in the copolymers is affected by the amount of the SCB in the backbone of the polymer chain. Initially, the SCB move to the folding surface. Once the SCB are located near the folding surface the order starts to grow. In all cases here shown, the C₄ branches are excluded from the ordered domains. To take into account, the influence of the branch distribution, a different branch distribution model has been considered for the two‐branched systems. The crystallization fraction (α) and the density of the amorphous and ordered fractions was defined using the local‐bond order parameter. Both magnitudes decrease as the number of branches increases. These facts fairly agree with experimental literature data. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

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     

Monte Carlo Simulation of the Topology and Conformational Behavior of Hyperbranched Molecules: Pd–Diimine‐Catalyzed Polyethylene

A kinetic Monte Carlo model was developed to simulate the polymerization of ethylene with palladium–α‐diimine catalyst wherein hyperbranched molecules are formed through a chain‐walking mechanism. The total degree of branching and the distribution of short branches obtained with the model agree well with reported ¹³C NMR experimental results. Different chain topologies were generated by varying the probability of chain walking, P_w , which controls the competition between chain‐walking and monomer insertion. Molecular Monte Carlo simulations were subsequently conducted to study the conformations of isolated molecules (created by the kinetic Monte Carlo scheme) to relate molecular shape and topology. Our results provide evidence that the topology varies from predominantly linear with many short branches at low P_w to a densely branched, globular structure at high P_w . In contrast to experimental observations, our results for the molecular weight (N) dependence of the radius of gyration (R_g ∝ N^v) indicate that the branching topology has an effect on this relation, i. e., high‐P_w molecules have a smaller scaling exponent v. The simulated N‐dependence of the second virial coefficient exhibits a similar behavior. We also discuss the unusual conformational behavior of highly branched polymers obtained when P_w → 1.     

Phase behavior of low molecular weight polyethylenes from homogeneous and heterogeneous solutions

The pseudophase diagrams of solutions of low molecular weight polyethylene (PE) (number‐average molecular weight < 1500 g/mol) in octamethyl cyclotetrasiloxane (OCTS) and isododecane (IS) were determined by direct observation of cloud points and optical microscopy. In addition, melting temperatures were also determined by differential scanning calorimetry. In the range of single liquid–solid transitions, the data conformed to the classical melting temperature composition relation as a result of the formation of extended crystallites. The melting data were used to determine the interaction parameter of the PE in OCTS (1.4 ± 0.1) and IS (0.22 ± 0.05). The structural and thermal properties of the gels formed by a competing liquid–liquid and liquid–solid phase separation, under nonequilibrium conditions, contrast with the properties of the crystals formed from a single liquid–solid transition. Coarsening within the liquid phases was evidenced by optical microscopy, and insights about the mechanism of the kinetics of the coarsening process are given. The temporal changes of the melting temperature of crystallites formed from the heterogeneous phase (OCTS) reveal dynamics within a nonequilibrium state. In contrast, the crystallites formed from a homogeneous solution (IS) showed negligible melting‐temperature changes with time. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 878–889, 2002     

Direct Participation of Solvent Molecules in the Formation of Supramolecular Polymers

This article reports supramolecular polymerization of two bis-amide functionalized naphthalene-diimide (NDI) building blocks (NDI−L and NDI−C) in two solvents, namely n-heptane (Hep) and methylcyclohexane (MCH). NDI−L and NDI−C differ only by the peripheral hydrocarbon wedges, consisting of linear C7 chains or cyclic methylcyclohexane rings, respectively. UV/Vis and FTIR spectroscopy studies reveal distinct internal order and H-bonding pattern for NDI−L and NDI−C aggregates irrespective of the solvent system, indicating the dominant role of the intrinsic packing parameters of the individual building block, possibly influenced by the peripheral steric crowding. However, NDI−L produces a significantly stronger gel in Hep compared to MCH as evident from the rheological and thermal properties. In contrast, NDI−C exhibits a clear preference for MCH, producing gel with moderate strength but in Hep it fails to produce 1D morphology or gelation. All-atom molecular dynamics (MD) simulation studies corroborate with the experimental observation and provide the rationale for the observed solvent-shape effect by revealing a quantitative estimate regarding the thermodynamics of self-assembly in these four combinations. Such clear-cut shape-matching effect (between the peripheral hydrocarbon wedge and the solvent system) unambiguously support a direct participation of the solvent molecules during supramolecular polymerization and presence of a closely-adhered solvent shell around the supramolecular polymers, similar to the first layer of water molecules around the protein surface. Solvent induced CD experiments support this hypothesis as induced CD band was observed only from a chiral co-solvent of matching shape. This is reconfirmed by the higher de-solvation temperature of the shape-matching NDI/solvent system combination compared to the shape mis-match combination in variable temperature UV/Vis experiments, revealing transformation to a different aggregate at higher temperatures rather than disassembly to the monomer for all four combinations.     

Investigation of the Variation of Unit Cell Dimensions of Crystalline Polymers with High‐Resolution FT‐IR Spectroscopy

Summary: High‐resolution FT‐IR spectroscopy has been used for the first time to characterize the variation of the unit cell dimensions of high‐density polyethylene (HDPE). In combination with the unit cell parameters of HDPE measured at different temperatures by Swan using wide‐angle X‐ray diffraction, the relationship between the rocking band shift (730 cm⁻¹) and the change of the unit cell volume of HDPE has been established.

High‐resolution variable‐temperature FT‐IR spectra of HDPE rocking bands with decreasing temperature.     

Ultraviolet grafting of methacrylic acid and acrylic acid on high‐density polyethylene in different solvents and the wettability of grafted high‐density polyethylene. I. Grafting

Methacrylic acid (MAA) and acrylic acid (AA) were grafted onto high‐density polyethylene (PE) with UV initiation and a range of solvents. With acetone as the solvent, MAA was more easily grafted onto PE when the photoinitiator benzophenone was precoated on PE than when it was dissolved in the monomer solution. The grafting was faster in aliphatic solvents than in polar solvents or a UV‐adsorbing aromatic solvent (toluene). Acetone itself could initiate the photografting of both MAA and AA onto PE when it was mixed with water. The extent of grafting of MAA onto PE showed a maximum when there was about 40% acetone in the mixture. For AA, when the acetone/water concentration was 10%, the extent of grafting increased rapidly with the irradiation time. At higher acetone concentrations, the extent of grafting was low. Atomic force microscopy images showed that the surface topography of PE grafted with MAA in acetone/water was quite different from that obtained when the grafting was performed in other organic solvents. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 253–262, 2004     

Connecting Linear Polymers Molecular Structure to Viscoelastic Properties and Melt Flow Index

A modeling pathway and software tool for linking entangled linear polymer molecular properties to linear viscoelasticity and melt index (MI) values is presented. A reptation model links molecular properties to the flow curve, and then, an ANSYS Polyflow model calculates MI values based on the flow curve predicted. The method is thoroughly tested and validated for uni‐ and bimodal, low‐ and high‐density polyethylene grades. An overall accuracy level in the range of 90% on average is exhibited, considering both model prediction steps: (i) molecular weight distribution to flow curve and (ii) flow curve to MI.

     

The mechanism and a slip model for the initial plastic deformation of amorphous polyethylene under uniaxial tension

The mechanical behaviors of a polyethylene (PE) bulk consisting of amorphous molecular chains under uniaxial tension have been explored using molecular simulations. The stress–strain relationship and the plastic deformations of the PE bulk have been analyzed. Two deformation stages were found in the stress–strain curve, the elastic stage with a straight linear part of the curve and the plastic stage with a flat sawtooth‐like part. The Young's modulus calculated from the elastic part is in good agreement with experimental results. Some key parameters such as the energy variations in different terms reveal that the interchain slip should be chiefly responsible for the initial plastic deformations of amorphous PE under uniaxial tension. In order to address how this slip influences the plastic deformations, the mechanical details of a single chain have been elucidated when it was pulled out from two PE clusters consisting of regular and amorphous chains, respectively. The interchain slip, found as the basic movement style, is responsible for the movement of the stretched chain. Both the critical slip force and the critical slip length have been found in these two cases. For the straight chain pulled out from the cluster with regular chains, the critical slip force is about 1.81 nN and the critical slip length is about 40 polymerization degrees. While for the chain in the amorphous cluster, the critical force is about 0.86 nN and the critical length is almost the same. Based on the simulation results, a meso slip model has been deduced to explain the behaviors of the amorphous PE bulk under uniaxial tension. With reference to the slip model of single crystals and polycrystals a constitutive relation was obtained by considering the Young's modulus, the equivalent slip stress and the average orientation parameters of each chain. The comparison of the results from the constitutive relation and the simulations proves that this model does well in predicting the mechanical behaviors of amorphous PE under uniaxial tension in general. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 986–998     

The AFM observation of linear chain and crystalline conformations of ultrahigh molecular weight polyethylene molecules on mica and graphite

Atomic force microscopy (AFM) has been applied to visualize expanded linear chain and compact crystalline conformations of ultrahigh molecular weight polyethylene (PE) molecules deposited on mica and graphite from diluted solutions at elevated temperatures. Isolated PE chains are visualized on mica with the apparent negative AFM height and the contour length much shorter than the molecular length. The chain conformations have both the kinked random‐coil sites and the sites of the unexpectedly large two‐dimensional expansion. The crystalline conformations on mica are small single‐molecule rod‐like nanocrystallites and the isolated block‐type “edge‐on” nanolamellae comprising several PE molecules. Noticeable fluctuations of the fold length in the range of approximately 10–20 nm around the averaged value of about 15 nm are observed for nanocrystallites and on tips of some nanolamellae. The explanation of the experimentally observed features of chain surface conformations on mica is proposed. It implies the immobilization of PE molecules in the nm‐thickness salt layer formed on mica surface at ambient conditions after PE deposition and the presence along the chain of multiple expanded chain folds. Only isolated lamellae and lamellar domains of a monolayer height are observed on graphite samples. The substrate/polymer epitaxial incommensurability important for the observation of the PE linear chain surface conformations is discussed from the comparison of the results obtained for mica and graphite, the coil‐to‐crystal intramolecular transformation is assumed to be inhibited on mica surface. The slow disintegration of the original gel structure of PE stock‐solution used for the high‐temperature depositions was found to result in the characteristic large‐scale morphological heterogeneity of the samples. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 766–777, 2010     

Estimation of Self‐Diffusion Coefficients of Small Penetrants in Semicrystalline Polymers Using Single‐Sided NMR

A simple and fast way to measure proton self‐diffusion coefficients of small penetrant molecules in semicrystalline polymers is introduced. The approach takes advantage of the strong static gradient of a mobile single‐sided NMR sensor and it is demonstrated on PE samples with varying degrees of crystallinity fully saturated in either toluene or n‐hexane. The self‐diffusion coefficients were measured using the gradient stimulated echo sequence appended with a CPMG. It is also shown for the first time, with demonstration on PE plates several millimeter thick with different aging histories, that one‐dimensional profiles of self‐diffusion coefficients as a function of depth can be easily obtained.     

Study of the composition and morphology of new modifications of titanium‐magnesium catalysts with improved properties in ethylene polymerization

Data on new modifications of supported titanium‐magnesium catalysts (TMCs) with improved performance in ethylene polymerization are reported. These catalysts possess a high and stable activity, an enhanced ability to regulate molecular weight of the polymer by hydrogen, a controllable particle size at a narrow particle size distribution, and the ability to produce the polymer with an increased bulk density. Various physicochemical methods were used to obtain data on the chemical composition of novel supports and catalysts, their phase composition and crystal structure as well as the pore structure. The results obtained were used to discuss possible correlations between composition and structure of TMCs and their catalytic properties. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2545–2558     

Molecular model for solubility of gases in flexible polymers

We propose a model for a priori prediction of the solubility of gases in flexible polymers. The model is based on the concept of ideal solubility of gases in liquids. According to this concept, the mole fraction of gases in liquids is given by Raoult's law with the total pressure and the vapor pressure of the gas, where the latter may have to be extrapolated. However, instead of considering each polymer molecule as a rigid structure, we estimate the effective number of degrees of freedom from an equivalent freely jointed bead‐rod model for the flexible polymer. In this model, we associate the length of the rods with the molecular weight corresponding to a Kuhn step. The model provides a tool for crude estimation of the gas solubility on the basis of only the monomer unit of the polymer and properties of the gas. A comparison with the solubility data for several gases in poly(dimethylsiloxane) reveals agreement between the data and the model predictions within a factor of 7 and that better model results are achieved for temperatures below the critical temperature of the gas. The model predicts a decreasing solubility with increasing temperature (because of the increasing vapor pressure) and that smaller gas molecules exhibit a lower solubility than larger ones (e.g., CH₄ has a smaller solubility than CO₂), which agrees with the experimental data. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 701–706, 2003     

Understanding Creep Behavior of Semicrystalline Polymer via Coarse‐Grained Modeling

Understanding the deformational and failure behaviors of thermoplastic semicrystalline polymers is crucial due to the practical usages in various engineering applications. Taking isotactic polypropylene (iPP) as a semicrystalline polymer model system, atomistically informed coarse‐grained (CG) molecular dynamics (MD) simulations are employed to investigate the creep behavior of iPP. The simulations reveal that there exists a threshold stress of about 20.0 MPa, above which the maximum strain of iPP within the simulation time span increases dramatically. From the strain‐time analysis, it is observed that the iPP exhibits an initial elastic deformation stage and a subsequent plastic stage at lower stress levels, while a three‐stage creep behavior including a third fracture stage is observed at higher stress levels. Specifically, at lower stress levels, the bonded energy increases continuously as the chains stretch steadily, while the nonbonded energy shows an initial increase followed by a steady decrease due to the interchain sliding. At higher stress levels, both bonded and nonbonded energies change dramatically at the third stage, resulting from accelerated chain stretching, unfolding, sliding, and breaking. This study provides physical insight into the creep behavior of iPP at a fundamental molecular level and highlights the important role of microstructural evolution of chains in the deformation of semicrystalline polymer materials. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1779–1791     

A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations

Molecular mechanics models have been applied extensively to study the dynamics of proteins and nucleic acids. Here we report the development of a third-generation point-charge all-atom force field for proteins. Following the earlier approach of Cornell et al., the charge set was obtained by fitting to the electrostatic potentials of dipeptides calculated using B3LYP/cc-pVTZ//HF/6-31G** quantum mechanical methods. The main-chain torsion parameters were obtained by fitting to the energy profiles of Ace-Ala-Nme and Ace-Gly-Nme di-peptides calculated using MP2/cc-pVTZ//HF/6-31G** quantum mechanical methods. All other parameters were taken from the existing AMBER data base. The major departure from previous force fields is that all quantum mechanical calculations were done in the condensed phase with continuum solvent models and an effective dielectric constant of epsilon = 4. We anticipate that this force field parameter set will address certain critical short comings of previous force fields in condensed-phase simulations of proteins. Initial tests on peptides demonstrated a high-degree of similarity between the calculated and the statistically measured Ramanchandran maps for both Ace-Gly-Nme and Ace-Ala-Nme di-peptides. Some highlights of our results include (1) well-preserved balance between the extended and helical region distributions, and (2) favorable type-II poly-proline helical region in agreement with recent experiments. Backward compatibility between the new and Cornell et al. charge sets, as judged by overall agreement between dipole moments, allows a smooth transition to the new force field in the area of ligand-binding calculations. Test simulations on a large set of proteins are also discussed.     

A molecular‐level computational study of the diffusion and solubility of water and oxygen in carbonaceous polyethylene nanocomposites

Monte Carlo and molecular dynamics simulations were performed to investigate the effect on the solubility, diffusion, and permeability of water and oxygen when adding graphene or single‐walled carbon nanotubes (SWCNTs) to polyethylene (PE). When compared with pure PE, addition of graphene lowered the solubility of water, whereas at lower temperatures, the oxygen solubility increased because of the oxygen–graphene interaction. Addition of SWCNTs lowered the solubility of both water and oxygen when compared with pure PE. A detailed analysis showed that an ordered structure of PE is induced near the additive surface, which leads to a decrease in the diffusion coefficient of both penetrants in this region. The addition of graphene does not change the permeation coefficient of oxygen (in the direction parallel to the filler) and, in fact, may even increase this coefficient when compared with pure PE. In contrast, the water permeability is decreased when graphene is added to PE. The addition of SWCNTs decreases the permeability of both penetrants. Graphene can consequently be added to selectively increase the solubility and permeation of oxygen over water, at least at lower temperatures. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 589–602     

Volume‐exclusion effects in polyethylene blends filled with carbon black,graphite, or carbon fiber

Conductive polymer composites possessing a low percolation‐threshold concentration as a result of double percolation of a conductive filler and its host phase in an immiscible polymer blend afford a desirable alternative to conventional composites. In this work, blends of high‐density polyethylene (HDPE) and ultrahigh molecular weight polyethylene (UHMWPE) were used to produce ternary composites containing either carbon black (CB), graphite (G), or carbon fiber (CF). Blend composition had a synergistic effect on electrical conductivity, with pronounced conductivity maxima observed at about 70–80 wt % UHMWPE in the CB and G composites. A much broader maximum occurred at about 25 wt % UHMWPE in composites prepared with CF. Optical and electron microscopies were used to ascertain the extent to which the polymers, and hence filler particles, are segregated. Differential scanning calorimetry of the composites confirmed that the constituent polymers are indistinguishable in terms of their thermal signatures and virtually unaffected by the presence of any of the fillers examined here. Dynamic mechanical analysis revealed that CF imparts the greatest stiffness and thermal stability to the composites. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1013–1023, 2002