Finitely extensible nonlinear elastic potential

Figure 1.41. Potential energies for the bead-spring model LJ1—Lennard-Jones potential LJ2—van der Waals potential EXP1, EXP2—short-range polar potential FENE—finitely extensible nonlinear elastic potential.

The Gaussian bond (1.4) can easily be stretched to high extension, and allows unphysical mutual passing of bonds. To prevent this unreaUstic mechanical property, the model potential, called the finitely extensible nonlinear elastic potential (FENE), and described by... 

Lee et al. [21] conducted molecular dynamics simulations of the flow of a com-positionally symmetric diblock copolymer into the galleries between two siUcate sheets whose surfaces were modified by grafted surfactant chains. In these simulations they assumed that block copolymers and surfactants were represented by chains of soft spheres connected by an finitely extensible nonlinear elastic potential, non-Hookean dumbbells [22], which had been employed earlier in the simulations of the dynamics of polymer blends and block copolymers by Grest et al. [23] and Murat et al. [24]. To describe the interactions among the four components, namely the surfaces, the surfactant, and two blocks, Lee et al. [21] employed a Lennard-Jones potential having the energy parameters which are associated with the type of interactions often employed for lattice systems such as in the Flory-Huggins theory. 

LJl) and van der Waals (LJ2) potentials were used for nonpolar bead-bead and bead-wall interactions, respectively. For polar interactions, exponential potential functions (EXP 1,2) were added to both bead-bead and bead-wall cases. For the bonding potential between adjacent beads in the chain, a finitely extensible nonlinear elastic (FENE) model was used. For example, PFPE Zdol... 

In case of tetrahedral non polar liquid i.e. methane) each molecule in CG level represented by one bead and atomistically the molecule consisted of four atoms. The non-bonded interactions between the atoms were treated by Weeks-Chandler-Andersen potential (potential form is given in equation 38) and bonded interaction of all the atoms of a molecules by finitely extensible nonlinear elastic bonds as given in equation 39. 

The bond potential within the confinement region r,, + — ro < R (the total symmetric fluctuation width is 2R and centered about ro) is typically modeled by the finitely extensible nonlinear elastic (FENE) potential [50], which we introduce here in the form [51]... 

The mesoscale model consists of a set of crosslink nodes (i.e., junctions) connected via single finite-extensible nonlinear elastic (FENE) bonds (that can be potentially cross-linked and/or scissioned), which represent the chain segments between crosslinks. In addition, there is a repulsive Lennard-Jones interaction between all crosslink positions to simulate volume exclusion effects. The Eennard-Jones and FENE interaction parameters were adjusted and the degree of polymerization (p) for a given length of a FENE bond calibrated until the MWD computed from our network matched the experimental MWD of the virgin material [112]. 

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 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. 

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