= Membrane bending rigidity
{title2=$\kappa$}
This coefficient multiplies the squared mean-curvature term $\frac\kappa2\int(2H-C_0)^2dA$ in the <Helfrich membrane energy>. It has units of <energy>, unlike a beam's flexural rigidity. For small height modes of a nearly flat membrane of area $A$, with Fourier normalization $h_q=A^{-1}\int h(\mathbf x)e^{-i\mathbf q\cdot\mathbf x}d^2x$, quadratic bending and <tension> energies give $\langle|h_q|^2\rangle=k_BT/[A(\kappa q^4+\sigma q^2)]$ by the <equipartition theorem>. Thermal-flicker measurements can therefore separate short-wavelength bending from longer-wavelength tension effects.
Back to article page
