# softmatter:FENE Spring

Finitely extensible non-linear elastic (FENE) springs are often used in bead spring models of polymeric materials.

$U_{FENE} = \begin{cases} -0.5kR_{0}^2ln\left[1-\left(\frac{r}{R_{0}}\right )^2 \right ] & r

where r is the distance between neighboring beads, k is the energy parameter and R0 is the maximum length of the spring. Typically the values f k = 30 and R0 = 1.5σ are used in simulation, where σ is the diameter of the particle. These values ensure relatively stiff bonds and prevent unphysical chain crossings.

In many simulation packages particle-particle interactions between bonded pairs are not calculated, and thus to avoid particles sitting on top of each other, the Weeks-Chandler-Andersen is often included in the spring potential calculation:

$U_{FENE} = \begin{cases} U_{WCA} + -0.5kR_{0}^2ln\left[1-\left(\frac{r}{R_{0}}\right )^2 \right ] & r

"U"WCA is a Weeks-Chandler-Anderson volume-excluding repulsive force that balances the purely attractive logarithmic term.

## References

• G. S. Grest and K. Kremer, "Molecular dynamics simulation for polymers in the presence of a heat bath," Phys. Rev. A., 33, 3628-3631, (1986)