= Analytical ultracentrifugation
{title2=AUC}
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Analytical ultracentrifugation observes concentration profiles during rotation, rather than only recovering a separated pellet. Sector-shaped sample cells rotate past optical detectors. Absorbance scans measure attenuation at selected radii. A <Rayleigh interferometer> compares a sample sector with a solvent reference, converting concentration-dependent refractive-index changes into fringe shifts. Repeating scans follows a sedimentation boundary or the approach to a stationary distribution.<Optical Systems Used for AUC by Beckman Coulter Life Sciences>[Radial concentration scans, synchronized absorbance detection and reference-sector interference]{ref}
For a dilute solute of buoyant mass $m_b$ and translational friction $f_h$, radial force balance gives $s=m_b/f_h$, where $s$ is the <sedimentation coefficient>. <Diffusion> supplies $D=k_BT/f_h$. A velocity experiment resolves boundary motion and broadening; a <sedimentation equilibrium> experiment instead measures $d\ln c/d(r^2)=m_b\omega^2/(2k_BT)$. This follows from the <Boltzmann distribution> in centrifugal potential $-m_b\omega^2r^2/2$. The two approaches separate frictional size information from buoyant mass information; shape, hydration and solvent properties must be specified to infer a unique geometric dimension.
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