FENE-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... 

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

FENE Finite extensible non-linear elastic potential... 

We now present results from molecular dynamics simulations in which all the chain monomers are coupled to a heat bath. The chains interact via the repiflsive portion of a shifted Lennard-Jones potential with a Lennard-Jones diameter a, which corresponds to a good solvent situation. For the bond potential between adjacent polymer segments we take a FENE (nonhnear bond) potential which gives an average nearest-neighbor monomer-monomer separation of typically a 0.97cr. In the simulation box with a volume LxL kLz there are 50 (if not stated otherwise) chains each of which consists of N -i-1... 

The open/filled symbols correspond to extensible and nonextensible chains, respectively, which is controlled within the simulation by the strength of the FENE bond potentials. As one can see, for large values of the parameter combination N(p a fi/ /Rf the data saturate at a plateau and are thus in agreement with the scaling prediction... 

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 addition, the bonds between neighboring monomers as well as cross-linked monomers are assumed to obey the Fene potential and harmonic cosine bending potential, respectively ... 

Bonded potentials Interactions between two or more specific particles include FENE and harmonic bond potentials, bond angle and dihedral interactions. Again, potentials can also be included as tables. 

A simple generic bead spring model of chains can be used to study universal polymer properties that do not depend on specific chemical details. Bonds between neighbouring Lennard-Jones particles in a chain can be represented by the finite extension non-linear elastic (FENE) potential. 

Here, 1/bb represent the bonds between consecutive backbone sites, which are connected by nonlinear elastic springs (FENE). The functional form of the potential is given by... 

Other solutions for the singlet configuration-space distribution function are those for the steady-state, homogeneous potential flow of elastic dumbbells with any kind of spring (DPL, Eq. (13.2-14)), and the first few terms in a perturbation solution for steady-state, homogeneous flow of FENE dumbbells (DPL, Eq. (13.2-15)). 

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... 

FENE potentials. A treatment of a plane Poiseuille flow similar to the plane Couette flow considered here is feasible. The influence of confining... 

The FENE model with short chains of ten beads interacting with a truncated Lennard-Jones potential has been used for an MD investigation (381,382) of mode coupling theory just above the predicted critical temperatiue, which in turn is above the Tg. It is too early to say whether this theory will prove to be of practical use for polymer science, but simulations of this kind are probing deeply into the natiue of the glass transition, which can only help to illiuninate the physics of this important transition. 

Polyelectrolytes. Multiple chain polyelectrolytes (qv) have been simulated by Limbach and Holm (419). They nsed a FENE model having beads that interact with both a truncated LJ potential and an electrostatic potential. Counte-... 

The parameters e and <7 are chosen as units of energy and length, respectively. The bonded forces are given by the FENE potential with J o= 1.5(7 and fe = 30e/(7. These particular parameters are chosen to prevent chains crossing themselves as weU as other drains (see below). Note that the bonded beads experience the sum of attractive FENE and repulsive LJ potentials, which can also tre approximated by eqn [43]. 

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... 

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