Finitely extendible nonlinear elastic

Nearest neighbors along a chain interact by means of a FENE (finitely extendible nonlinear elastic) potential... 

In addition to the excluded volume interaction, one also needs to add an attractive interaction binding the beads along the chain and for polymer brushes a wall-monomer interaction. The specific form of these interactions is not critical, except that the interaction between bonded beads should be such that the maximum extent of the bond is small enough such that bond crossing is inhibited. For the simulation results presented here, the finite extendible nonlinear elastic (FENE) model first introduced by Bird et al. [114] with suitably modified parameters [46,115] to avoid bond crossing was used. 

This process has been examined theoretically by a number of authors (29-31), who derived constitutive equations based upon finitely extendable nonlinear elastic (FENE) dumbbell models (29), bead-rod models (30), and bead-spring models (31). There is general agreement that a large increase in elongational viscosity should be expected. 

FENE finitely extendable nonlinear elastic model... 

The examples of non-Newtonian microchannel flows cited in the present article so far inherently assume that the continuum hypothesis is not disobeyed, so far as the description of the basic governing equations is concerned. This, however, ceases to be a valid consideration in certain fluidic devices, in which the characteristic system length scales are of the same order as that of the size of the macromolecules being transported. Fan et al. [10], in a related study, used the concept of finitely extended nonlinear elastic (FENE) chains to model the DNA molecules and employed the dissipative particle dynamics (DPD) approach to simulate the underlying flow behavior in some such representative cases. From their results, it was revealed that simple DPD fluids essentially behave as Newtonian fluids in Poiseuille flows. However, the velocity profiles of FENE... 

The (two-dimensional) model for a relatively stiff molecule subjected to a simple shear flow, on the one hand, shows many features observed in NEMD simulations of finitely extendible nonlinear elastic (FENE) chain molecules. On the other hand, the dynamics found for the simple model is intriguingly complex and it deserved a careful study on its own. It seems appropriate also to analyse the system at higher temperatures. Furthermore, the model provides a convenient test bed for various thermostats other and additional thermostats, e.g. based on deterministic scattering [22] should be tested. Obvious extensions of the present model may involve other potential functions of nonlinear elastic type such as = (1/2) -I- (1/4) or = (1/4) (1 — r ) as well as... 

The dumbbell is thus called the FENE-P dumbbell ( FENE stands for Finite Extendable Nonlinear Elastic , and P stands for Peterlin, who first suggested this simplification). With this approximation, the Kramers formulation becomes... 

As discussed in previous chapters, the choice of the bond / o rf( r/ ) and short-range —r l) potential varies from simulation to simulation. Off-lattice models, for example, have used the harmonic-spring potential, the FENE (finitely extendable, nonlinear elastic) potential, the rigid bond with fixed valence angles, and the freely-jointed chain model to represent the bonding interaction between adjacent monomers. For the short-range... 

The simulation techniques used for polyelectrolytes in solution are extensions of the standard methods used for neutral polymers. The polymer chain is modeled as a set of connected beads. The beads are charged depending on the charge fraction, but otherwise the details of the monomer structure are neglected. Various means of connecting the bonded monomers are used. In lattice Monte Carlo the bonds are of course fixed. Two sets of simulations have used the rotational isomeric state model. Other simulations have used Hookean springs or the finite-extendable-nonlinear-elastic (FENE) potential. No important dependence on the nature of the bonds is expected at this level of modeling the polymer chain. 

H. R. Warner, Jr., Kinetic Theory and Rheology of Dilute Suspensions of Finitely Extendible Dumbbells, Ind. Eng. Chem. Fundam., 11,379-387 (1972) also, R. L. Christiansen and R. B. Bird, Dilute Solution Rheology Experimental Results and Finitely Extensible Nonlinear Elastic Dumbbell Theory, J. Non-Newt. Fluid Mech., 3, 161-177 (1977/1978). 

One important issue in dealing with the nonlinear viscoelastic response of materials is the amount of data needed to determine the material parameters in the models. As noted above, even the general finite elasticity theory requires significant work to obtain the material parameters over the full three-dimensional deformation space. This is one reason that the VL framework is so attractive, when it works. Therefore, it is of interest to investigate whether or not the model can be extended to include compressibility. Pesce and McKenna (146) performed torsional tests on polycarbonate as described above. They then asked whether the VL function could be used to predict the tension and compression responses of the material. An important assumption in their approach was that the VL function determined from the torsional measurements using equations 45, 46, 47, 48, 49, 50, 51 (described immediately above) could be used to predict uniaxial data. When the incompressible equations 50 were applied to try to estimate the uniaxial stress-deformation data (isochronal), these equations did not work. However,... 

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