FENE

FENE stands for Finite Extensible Nonlinear Elastic. It is a model used in polymer physics to describe the entropic elasticity of polymer chains in bead-spring representations, capturing the idea that a polymer spring cannot extend beyond a finite length.

In the FENE model, a polymer is represented as beads connected by a nonlinear spring. For a dumbbell with end-to-end vector r, the FENE potential energy is U_FENE(r) = - (1/2) k R0^2 ln(1 - (r^2 / R0^2)), where R0 is the maximum extension and k is the spring constant. The corresponding force is F(r) = - dU_FENE/dr = - k r / (1 - (r^2 / R0^2)). As r approaches R0, the force diverges, which prevents unphysical overstretching and enforces finite extensibility.

The FENE potential is commonly used in coarse-grained bead-spring models of polymers, often paired with nonbonded interactions such as Lennard-Jones to capture excluded volume. It has become a standard choice for simulating polymer dynamics and rheology, particularly in non-equilibrium flows and in studies of entangled melts.

Variants and extensions include FENE-P, which applies a Peterlin closure to derive a closed set of equations for the polymer conformation tensor, enabling tractable modeling of viscoelastic polymer solutions and flows. The FENE family remains widely used because it provides a simple, physically motivated way to incorporate finite chain extensibility into simulations while preserving computational efficiency.

Historically, the FENE model was popularized in bead-spring polymer simulations by Kremer and Grest and has since become a foundational element in computational polymer science.

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