The chemo-mechanical coupling behavior of hydrogels incorporating entanglements of polymer chains

To describe precisely the chemo-mechanical coupling behavior of hydrogels, a general form of free energy density function is presented by considering chain entanglements and functionality of junctions. We use the chemical potential of the solvent and the deformation gradient of the network as the independent variables of the developed free energy function, and implement this material model in the finite element package, ABAQUS, to analyze several examples of chemo-mechanical equilibrium deformation behaviors of hydrogels. The influence of chain entanglements and junction functionality on the chemo-mechanical behavior of hydrogels is addressed based on our simulation. With the coded subroutine UHYPER, this work may provide a numerical tool to study complex phenomena in hydrogels.     

Novel rheological features of molten SEBS copolymers: Mechanical relaxation at low frequencies and flow split

Poly(styrene)-poly(ethylene-co-butylene)-poly(styrene) (SEBS) triblock copolymers with a PS volume fraction ? = 0.30 are investigated. The analysis of the loss tangent at low frequencies leads to define a mechanical relaxation associated to the blocking effect of ordered PS cylinders on PEB chains motion. Submitting SEBS to a shear flow at 250 °C an orientation of the cylinders is observed. The effect of the molecular weight and the cylinder alignment on the relaxation is studied. Continuous flow experiments, in torsion and capillary mode, reveal the presence of very severe surface cracks which cause the phenomenon called “flow split”. The correlation between dynamic viscoelastic results and flow split is investigated, concluding that this is related to an entanglement-disentenglement process, rather to an alignment effect of PS cylinders.     

Primitive chain network simulations for branched polymers

We present simulations of branched polymer dynamics based on a sliplink network model, which also accounts for topological change around branch points, i.e., for branch-point diffusion. It is well-known that, with the exception of stars, branched polymers may show a peculiar rheological behavior due to the exceptionally slow relaxation of the backbone chains bridging branch points. Though Brownian simulations based on sliplinks are powerful tools to study the motion of polymers and to predict rheological properties, none of the existing methods can simulate the relaxation of the bridge chains. The reason for that is lack of a rule for network topology rearrangement around branch points, so that entanglements between bridge chains cannot be renewed. Therefore, we introduce in this paper one possible branch-point mobility rule into our primitive chain network model. For star polymers, diffusion coefficients were calculated and compared with experiments. For both star and H-shaped polymers, diffusion was simulated both with and without the new rule, and the effect on linear viscoelasticity was also determined in one case.     

Electrophoretic mobility of linear and star-branched DNA in semidilute polymer solutions

Electrophoresis of large linear T2 (162 kbp) and 3-arm star-branched (N(Arm) = 48.5 kbp) DNA in linear polyacrylamide (LPA) solutions above the overlap concentration c* has been investigated using a fluorescence visualization technique that allows both the conformation and mobility mu of the DNA to be determined. LPA solutions of moderate polydispersity index (PI approximately 1.7-2.1) and variable polymer molecular weight Mw (0.59-2.05 MDa) are used as the sieving media. In unentangled semidilute solutions (c* < c < c(e)), we find that the conformational dynamics of linear and star-branched DNA in electric fields are strikingly different; the former migrating in predominantly U- or I-shaped conformations, depending on electric field strength E, and the latter migrating in a squid-like profile with the star-arms outstretched in the direction opposite to E and dragging the branch point through the sieving medium. Despite these visual differences, mu for linear and star-branched DNA of comparable size are found to be nearly identical in semidilute, unentangled LPA solutions. For LPA concentrations above the entanglement threshold (c > c(e)), the conformation of migrating linear and star-shaped DNA manifest only subtle changes from their unentangled solution features, but mu for the stars decreases strongly with increasing LPA concentration and molecular weight, while mu for linear DNA becomes nearly independent of c and Mw. These findings are discussed in the context of current theories for electrophoresis of large polyelectrolytes.     

Rheological properties of branched polystyrenes: nonlinear shear and extensional behavior

Nonlinear shear and uniaxial extensional measurements on a series of graft-polystyrenes with varying average numbers and molar masses of grafted side chains are presented. Step-strain measurements are performed to evaluate the damping functions of the melts in shear. The damping functions show a decreasing dependence on strain with an increase in mass fraction of grafted side chains. Extensional viscosities of the melts of graft-polystyrenes exhibit a growing strain hardening with increasing average number of grafted side chains as long as the side branches have a sufficient molar mass to be entangled. Graft-polystyrenes with side arms below the critical molar mass M _c for entanglements of linear polystyrene but above the entanglement molar mass M _e of linear polystyrene (M _e < M _w,br < M _c) still show a distinct strain hardening. With decreasing molar mass of the grafted side chains (M _w,br < M _e) the nonlinear-viscoelastic properties of the graft-polystyrene melts approach the behavior for a linear polystyrene with comparable polydispersity.Electronic Supplementary Material Supplementary material is available for this article at     

Monte Carlo Simulation of Thin Film Polymer Melts

We present Monte Carlo simulation data on conformations and dynamics of polymer melts confined in narrow slits of different widths and compare with data of bulk systems. We find that in confined geometries the chains swell laterally; they retain and even expand their spatially long-range correlations compared to bulk polymers and in contrast to the assumption of a complete screening of excluded volume. Long chains in bulk melts show entangled dynamics with a clear signature of a t^1/4-power law for the mean square displacements of innermost monomers at intermediate time scales. This behavior is gradually lost by confining the melts in slits with decreasing width. For ultra-thin films, the dynamics appears to follow a Rouse-like behavior over the entire subdiffusive regime. However, the terminal relaxation time is significantly increased compared to Rouse relaxation. This interesting observation was not reported previously and is the focus of our ongoing research.     

Analysis of the entanglements in carbon nanotube fibers using a self-folded nanotube model

Carbon nanotube (CNT) fibers have shown superb mechanical properties, and have high potential to be used as reinforcements in multifunctional composites. CNT entanglements always exist in CNT fibers and play a crucial role in affecting their mechanical properties. In this study, the CNT entanglement is modeled as two connecting self-folded CNTs (SFCNTs). At large aspect ratios, a CNT is energetically favorable to be self-folded due to the van der Waals interactions between different parts of the CNT. The geometrical characteristics of the SFCNTs, such as the critical length for self-folding as well as the critical effective width and length, are investigated by using both an exact theoretical model and an approximate theoretical model. The tensile properties of the SFCNTs have been examined by using both the approximate theoretical model and atomistic simulations. Good agreements are achieved in the results of these two approaches.     

Theoretical modeling of microstructured liquids: a simple thermodynamic approach

A new method is presented for accounting for microstructural features of flowing complex fluids at the level of mesoscopic, or coarse-grained, models by ensuring compatibility with macroscopic and continuum thermodynamics and classical transport phenomena. In this method, the microscopic state of the liquid is described by variables that are local expectation values of microscopic features. The hypothesis of local thermodynamic equilibrium is extended to include information on the microscopic state, i.e., the energy of the liquid is assumed to depend on the entropy, specific volume, and microscopic variables. For compatibility with classical transport phenomena, the microscopic variables are taken to be extensive variables (per unit mass or volume), which obey convection-diffusion-generation equations. Restrictions on the constitutive laws of the diffusive fluxes and generation terms are derived by separating dissipation by transport (caused by gradients in the derivatives of the energy with respect to the state variables) and by relaxation (caused by non-equilibrated microscopic processes like polymer chain stretching and orientation), and by applying isotropy. When applied to unentangled, isothermal, non-diffusing polymer solutions, the equations developed according to the new method recover those developed by the Generalized Bracket [J. Non-Newtonian Fluid Mech. 23 (1987) 271; A.N. Beris, B.J. Edwards, Thermodynamics of Flowing Systems with Internal Microstructure, first ed., Oxford University Press, Oxford, 1994] and by the Matrix Model [J. Rheol. 38 (1994) 769]. Minor differences with published results obtained by the Generalized Bracket are found in the equations describing flow coupled to heat and mass transfer in polymer solutions. The new method is applied to entangled polymer solutions and melts in the general case where the rate of generation of entanglements depends nonlinearly on the rate of strain. A link is drawn between the mesoscopic transport equations of entanglements and conformation and the microscopic equation describing the configurational distribution of polymer segment stretch and orientation. Constraints are derived on the generation terms in the transport equations of entanglements and conformation, and the formula for the elastic stress is generalized to account for reversible formation and destruction of entanglements. A simplified version of the transport equation of conformation is presented which includes many previously published constitutive models, separates flow-induced polymer stretching and orientation, yet is simple enough to be useful for developing large-scale computer codes for modeling coupled fluid flow and transport phenomena in two- and three-dimensional domains with complex shapes and free surfaces.     

Power law of nucleation rate of folded-chain single crystals of polyethylene

The number-average molecular weight (M _n) dependence of the primary nucleation rate (I) of polyethylene (PE) folded-chain single crystals was studied in the ordered phase. We observed that the M _n dependence of I is mainly controlled by the diffusion process of polymer chains within the interface between a nucleus and the melt and/or within the nucleus. The results show that I decreases with increasing M _n and follows a power law I∝M _n ^−2.3 for the ordered phase. It is named the power law of the nucleation rate. In a previous article we showed that for the disordered phase I∝M _n ⁻¹. In this article, we concluded that I decreases with increasing M _n and follows a universal power law, I∝M _n ^−H for both ordered and disordered phases. The power H depends on the degree of order of the crystalline phase, which is related to the morphology. Received: 13 September 2000 Accepted: 15 November 2000