softmatter:FENE Spring

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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<R_{0}\\ \infty & r \geq R_{0} \end{cases}

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<R_{0}\\ \infty & r \geq R_{0} \end{cases}

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


  • 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)
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