= Stretch and twist coefficients of an elastic filament
{title2=$K_b=k_BTA,\quad S=k_BTB,\quad K_t=k_BTC$}
For an <elastic filament> with reference arclength $s$, curvature $c$, axial <strain> $\epsilon$ and excess twist rate $\Omega$, a harmonic <energy> <density> is $(K_bc^2+S\epsilon^2+K_t\Omega^2)/2$. Bending and torsional rigidities have units of <energy> times <length>; the stretch modulus has units of <force>. Factoring out $k_BT$ therefore makes $A,C$ <lengths> but $B$ an inverse <length>. Axial <strain> under <tension> is approximately $F/S$. Twist is controlled by <torque> and rotational <boundary conditions>, not <force> alone. A three-dimensional thermally fluctuating <worm-like chain> has <persistence length> $K_b/(k_BT)$.
Back to article page
