Tensile Stress Generation on Crystallization of Polymer Networks (original) (raw)
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Journal of Polymer Science Part B: Polymer Physics, 1987
Polyurethane elastomers were prepared from a series of poly(ethylene oxide) samples by end-linking t h e chains into "model" trifunctional networks. The molecular weight M , between crosslinks in such networks is simply the number-average molecular weight M , of the precursor polymer. End-linking samples separately gave networks with unimodal distributions of network chain lengths, whereas end-linking mixtures of two sanlples having very different values of M, gave bimodal distributions with average values of M , equal to the average value of M,, for the two samples. Stress-strain isotherms in elongation were obtained for thesc networks, both unswollen and swollen to various extents. Strain-induced crystallization was manifestd in elastic properties t h a t changed significantly with changes in temperature. Swelling has more complicated effects, since it causes deformation of the network chains as well as melting of some of the crystallites. Comparisons among stress-strain isotherms a t constant M , indicate that bimodality facilitates strain-induced crystalli,mtion.
Polymer, 2018
To establish relationships between the molecular structure of polyolefines and their physical characteristics which determine possible commercial applications, structural changes and tensile deformation response up to deformations beyond the natural draw ratio were investigated using a variety of experimental approaches. True stress-strain curves were measured at different temperatures so as to estimate the available effective network density, which will eventually define the failure mode of the material under investigation. Analysis of the deformation by means of tensile strain hardening, assuming the Haward-Thackray spring dashpot decoupling assumption by means of Edward-Vilgis' non-Gaussian rubber-elastic slip-link model, reveals the role of transient and fixed network nodes. It was established by differential scanning calorimetry and X-ray diffraction analysis that the transformation from lamellar to fibrillar morphology passes through the several pronounced stages: deformation of initial lamellae ( < 1.5); destruction of lamellar structure through the tilt; slippage of molecules in the crystallites; simultaneous formation of fibrils with structural characteristics depending on the molecular structure and on deformation conditions; deformation of the formed fibrillar structure; tiltingformation of chevrons for high molecular weight low density polyethylene or slippage of fibrils and void formation. Distinction between fixed and transient slip link network contributions reveals neatly that although there is a slight drop in the fixed link network density with increasing temperature, this contribution remains Manuscript Click here to view linked References
Morphological changes during oriented polymer crystallization
Polymer Engineering and Science, 1976
A theory of the stress-induced crystallization of polymeric networks is presented which takes into account 1) the free energy of fusion, 2) crystal surface energies and 3) entropic changes in the amorphous sections of crystallizing chains. It is assumed that the vector running from one end to the other of the crystallite is oriented in the direction of network extension, irrespective of crystal morphology, thus minimizing the free energy of crystallization. Assuming that the network assumes the crystal morphology which minimizes the free energy ofthe network at a given degree of crystallinity and that the crystallization proceeds along this lowest free energy path, it is predicted for simple network extension that growth of a perfectly oriented extended-chain crystal occurs initially, changing to a one-fold crystal oriented perpendicular to extension at low extension and to a two-fold crystal having nearly perfect orientation at high extension. The stress is predicted to decay initially and then to rise as the network chains switch from an extended-to a folded-chain morphology. Spatial factors which may trap chains in the extended-chain morphology or prematurely stopping the crystallization process can result in a mixed crystal morphology. At high extension, the structure is similar to that of the shish kebab.
The Journal of Physical Chemistry B
A novel method is presented to build semi-crystalline polymer models used in molecular dynamics simulations. The method allows controlling certain aspects of the molecular morphology of the material. It relies on the generation of the polymer sections in the amorphous phase of the semi-crystalline structure according to the statistical polymer physics theory proposed by Adhikari and Muthukumar. 1 The amorphous phase is first built based on the method initially developed by Theodorou and Suter. 2 Then, the amorphous phase is stacked between crystallites, and a connection algorithm proposed by Rigby et al., 3 initially developed to build polymer thermosets, is employed to link two phases. For a given set of crystallinity degree, semi-crystalline long period, densities of the crystalline and amorphous phases and polymer molecular weight, the characteristic ratio is used to control the relative fractions of different types of polymer sections in the amorphous phase as well as the distribution of their lengths. There are three types of amorphous polymer sections: the ones that are reentering in the same crystallite called loops, those that are bonding two different crystallites called tie chains, and the chain tails ending in the amorphous region. The higher this characteristic ratio is, the higher the fraction of tie chains is. The full implementation of the theory is described and then applied to High-Density PolyEthylene (HDPE). Several samples are generated. The obtained structures are characterized. Their elastic coefficients are computed, and high uniaxial deformations are performed. It is shown that the higher the crystallinity degree, the higher the elastic coefficients. An entanglement analysis shows that the quantity of tie chains is more decisive than the entanglements in acting as stress transmitters to rigidify the structure.
A study of strain-induced crystallization of polymers
The response of polymers depends on their morphology. One of the challenges in modeling from a continuum perspective is how to incorporate the microstructural features into the homogenized continuum model. Here, we use a recent framework that associates dierent natural states and material symmetries with distinct microstructures of the body (Rajagopal, K.. We study the problem of strain-induced crystallization of polymeric materials, in particular, we study the problem of uniaxial stretching of polymeric materials and the subsequent crystallization and the predictions of the theory are compared with experimental results.
Cross-linked polymers in strain: Structure and anisotropic stress
arXiv (Cornell University), 2011
Molecular dynamic simulation enables one to correlate the evolution of the microstructure with anisotropic stress when a material is subject to strain. The anisotropic stress due to a constant strain-rate load in a cross-linked polymer is primarily dependent on the mean-square bond length and mean-square bond angle. Excluded volume interactions due to chain stacking and spatial distribution also has a bearing on the stress response. The bond length distribution along the chain is not uniform. Rather, the bond lengths at the end of the chains are larger and uniformly decrease towards the middle of the chain from both ends. The effect is due to the presence of cross-linkers. As with linear polymers, at high density values, changes in mean-square bond length dominates over changes in radius of gyration and end-to-end length. That is, bond deformations dominate over changes in size and shape. A large change in the mean-square bond length reflects in a jump in the stress response. Short-chain polymers more or less behave like rigid molecules. Temperature has a peculiar effect on the response in the sense that even though bond lengths increase with temperature, stress response decreases with increasing temperature. This is due to the dominance of excluded volume effects which result in lower stresses at higher temperatures. At low strain rates, some relaxation in the bond stretch is observed from = 0.2 to = 0.5. At high strain rates, internal deformation of the chains dominate over their uncoiling leading to a rise in the stress levels.
Intrinsic Deformation Behavior of Semicrystalline Polymers
Macromolecules, 2004
The influence of crystallinity and lamellar thickness on the intrinsic deformation behavior of a number of semicrystalline polymers is studied: a poly(ethylene terephthalate) and two different molecular weight grades of polyethylene and polypropylene. The crystallinity and lamellar thickness are altered by varying the rate of crystallization from the melt and by cold crystallization (annealing) at elevated temperatures above T g but below the melting point. Crystallinity and lamellar thickness are determined by wide-angle X-ray diffraction and small-angle X-ray scattering measurements. Uniaxial compression tests are performed to obtain the large strain intrinsic deformation behavior, e.g., yield stress, strain softening, and strain hardening modulus. The yield stress is found to be proportional to lamellar thickness, whereas the strain hardening modulus is shown not to depend on crystallinity or lamellar thickness. Over the strain range experimentally covered, the strain hardening modulus appears to be well described by a simple neo-Hookean relation and appears to be related to the chain entanglement density. An affirmation for this relation arises from the observation that slowly melt crystallized samples exhibit a lower strain hardening, resulting from a lower chain entanglement density, which is expected to be caused by reeling in of the molecular chains in such a slow crystallization process. The similarity in the results observed on all polymers tested supports the conclusion that the crystalline phase does not contribute to strain hardening, which is primary controlled by the chain entanglement density.
Deformation of semicrystalline polymers via crystal–crystal phase transition
Journal of Polymer Science Part B: Polymer Physics, 1988
A classification is given of flexible, semicrystalline polymers based on the early stage deformation behavior in the solid state. The criteria of each category are discussed with experimental evidence from the literature on 17 polymers. The central aim of this classification is to point out the possibility of ductility induced during deformation. The understanding of the induced ductility in a given semicrystalline polymer suggests a systematic route to optimize solid-state deformation processes for achieving high draw ratios.
Polymer, 2017
The influence of microstructure and temperature on the initiation of yield stress and strain of highdensity polyethylene are examined using a set of linear and branched polyethylenes. The polymers were crystallized in different ways in order to get samples covering the range of crystallinity 0.5 X c 0.8 and crystallite thickness 8 nm L c 29 nm. In contrast to the conventional macroscopic yield strain and stress, the initiation strain ε yi and stress s yi were estimated from the macroscopic stress-strain curves at the onset of local plasticity as judged from in situ WAXS experiments upon tensile deformation. Phenomenological linear relation was observed between s yi crystallinity at each draw temperature T d. The dislocation model was applied to check the correlation between s yi and crystal thickness. In order to also account for the chain topology, namely the concentration of stress transmitters ST, a modified Eyring's approach was proposed. This modelling provides a good prediction the s yi dependence on L c and ST in the context of thermally activated rate processes. Finally, anelastic stress gauge, s c cr , was determined from local strain measurements in crystals at the same local strain as for s yi. This critical elastic stress at initiation of crystal plasticity displayed a good correlation with s yi at high crystallinity. However, s c cr was found to deviate from s yi with increasing T d particularly at low X c values. This finding was attributed to the activation of the crystalline mechanical relation that involves a significant drop of s yi with increasing T d in the crystalline lamellae under shear yielding whereas it does not affect the theoretical s c cr elastic stress.