Cross-linked polymers in strain: Structure and anisotropic stress (original) (raw)
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Structure, molecular dynamics, and stress in a linear polymer
Mechanics of Materials, 2013
We present a study correlating uniaxial stress in a polymer with its underlying structure when it is strained. The uniaxial stress is significantly influenced by the mean-square bond length and mean bond angle. In contrast, the size and shape of the polymer, typically represented by the end-to-end length, mass ratio, and radius of gyration, contribu te negligibly. Among externally set control variables, density and polymer chain length play a critical role in influencing the anisotropic uniaxial stress. Short chain polymers more or less behave like rigid molecules. Temperature and rate of loadin g, in the range considered, have a very mild effect on the uniaxial stress.
Macromolecules, 2004
Polymer networks undergoing cross-linking reactions are studied using molecular dynamics simulations to investigate how the stress is influenced by the coupling between cross-linking and deformation. For networks cross-linked in the undeformed state, the modulus increases linearly with the cross-link density as expected from rubber elasticity theory. When cross-links are added to a network that was uniaxially deformed, the stress remains constant in accordance with the independent network hypothesis of Tobolsky. When the deformed network is subsequently released, permanent set is observed. Using the independent network hypothesis, together with the affine theory of rubber elasticity, a constitutive model is developed that accounts for the effect of the coupling between the cross-link density and strain histories of the network. The permanent set predictions from the affine model are higher than found from MD simulations.
Strain Hardening and Strain Softening of Reversibly Cross-Linked Supramolecular Polymer Networks
Macromolecules, 2011
Associative polymers have rich rheological behavior that fuels their use in a wide range of applications and motivates interest in the mechanisms that determine their behavior. 1À6 Their rheological properties can be categorized into two classes of viscoelastic response: 7 linear viscoelasticity, as normally measured by small amplitude oscillatory shear, and nonlinear viscoelasticity, such as that which occurs under high steady shear rate and large amplitude oscillatory shear. 7 In contrast to their linear rheological properties, the mechanisms underlying the nonlinear rheological properties of associative polymers vary from one system to another and are often unclear. As a result, extensive experimental and theoretical research has been devoted to the molecular origin of shear thickening and strain hardening of associative polymers. 8À18 At the core of the visoelastic response of associative polymers is the reversible association itself, and our group has previously demonstrated a useful method of probing the contributions of molecular reversibility to the macroscopic rheological properties of supramolecular polymer networks. 18À21 The method takes advantage of steric effects at the N-alkyl positions of N,C,N-pincer Pd(II) and Pt(II) complexes 17 through which the dissociation rate of the cross-linkers can be changed by orders of magnitude independently of the association constant. 22 Recently, the steady shear behavior of the metallo-supramolecular polymer networks formed by these bis-Pd(II) cross-linkers and poly(4-vinylpyridine) (PVP) was reported ( . The mechanism of shear thickening of samples in the semidilute unentangled regime and divergent shear thinning versus shear thickening of samples with identical structure but different cross-linker kinetics in the semidilute entangled regime were explored. We found that shear thickening was dominated by a conversion of intrachain to interchain bound cross-linkers but that the competition between reassociation of dissociated cross-linkers and polymer chain diffusion contributed to the efficiency of the conversion process. In this article, the large amplitude oscillatory shear (LAOS) behavior of the same metallo-supramolecular polymer networks is examined.
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.
Elasticity of cross-linked semiflexible biopolymers under tension
Physical Review E, 2013
Aiming at the mechanical properties of cross-linked biopolymers, we set up and analyze a model of two weakly bending wormlike chains subjected to a tensile force, with regularly spaced interchain bonds (cross-links) represented by harmonic springs. Within this model, we compute the force-extension curve and the differential stiffness exactly and discuss several limiting cases. Crosslinks effectively stiffen the chain pair by reducing thermal fluctuations transverse to the force and alignment direction. The extra alignment due to cross-links increases both with growing number and with growing strength of the cross-links, and is most prominent for small force f. For large f , the additional, cross-link-induced extension is subdominant except for the case of linking the chains rigidly and continuously along their contour. In this combined limit, we recover asymptotically the elasticity of a weakly bending wormlike chain without constraints, stiffened by a factor four. The increase in differential stiffness can be as large as 100% for small f or large numbers of cross-links.
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
The influence of cross-link coordination on the mechanical properties of polymers
2020
Reversible cross-linking is a powerful strategy employed by nature to specifically tailor the mechanical performance of load-bearing polymeric structures. These cross-links are found in a variety of biological systems such as bone, silk or mussel threads. They provide an efficient toughening mechanism due to hidden length unraveling and repeated rupture and reformation of cross-links during the course of deformation. In this dissertation, the main objective is to investigate the influence of cross-link coordination on the mechanical properties of polymeric structures. Three different structures are investigated: a single linear chain, fiber bundles and a stiff random network. The aim is to contrast the deformation behavior of polymers cross-linked with two-fold coordinated cross-links only (the "classical" system) with the behavior of system where three-fold coordination of cross-links is energetically most favorable. The inspiration for the current study stems from variou...
Elastic properties of randomly cross-linked polymers
Physical Review E, 1996
We have carried out extensive molecular-dynamics simulations of randomly cross-linked polymers and studied the onset of rigidity as the number of cross-links is increased. We find that for our systems, consisting of chains of length Nϭ10, 20, 30, and 50, the shear modulus E vanishes at a concentration of cross-links that is well above the geometric percolation threshold and that it seems to approach zero as Eϳ(nϪn c ) f , where the exponent f is considerably smaller than either the classical value f ϭ3 or the corresponding exponent tϷ2.0 of the conductivity of random resistor networks.
Molecular stress and strain in an oriented extended-chain polymer of finite molecular length
Macromolecules, 1995
ABSTRACT: We have developed constitutive and molecular mechanics models to investigate the influence of chain-end defects on the macroscopic tensile properties of extended-chain polymers of finite molecular weight. Molecular mechanics simulations have been performed on the rigid-rod polymer PBZO, poly@-phenylene benzobisoxazole), using the Dreiding I1 force field. The distance between chain ends (i, e., the chain length) can be varied systematically by increasing the size of the simulation unit cell in the chain direction ...