Spin-label Order Parameter Calibrations for Slow Motion

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Calibrations are given to extract orientation order parameters from pseudo-powder electron paramagnetic resonance line shapes of 14N-nitroxide spin labels undergoing slow rotational diffusion. The nitroxide z-axis is assumed parallel to the long molecular axis. Stochastic-Liouville simulations of slow-motion 9.4-GHz spectra for molecular ordering with a Maier–Saupe orientation potential reveal a linear dependence of the splittings, 2A_{hbox{max} } and 2A_{hbox{min} }, of the outer and inner peaks on order parameter S_{zz} that depends on the diffusion coefficient D_{{{text{R}} bot }} which characterizes fluctuations of the long molecular axis. This results in empirical expressions for order parameter and isotropic hyperfine coupling: S_{zz} = s_{1} times left( {A_{hbox{max} } - A_{hbox{min} } } right) - s_{o} and a_{o}^{{}} = tfrac{1}{3}left( {f_{hbox{max} } A_{hbox{max} } + f_{hbox{min} } A_{hbox{min} } } right) + delta a_{o}, respectively. Values of the calibration constants s_{1}, s_{text{o}}, f_{hbox{max} }, f_{hbox{min} } and delta a_{o} are given for different values of D_{{{text{R}} bot }} in fast and slow motional regimes. The calibrations are relatively insensitive to anisotropy of rotational diffusion (D_{{{text{R}}//}} ge D_{{{text{R}} bot }} ), and corrections are less significant for the isotropic hyperfine coupling than for the order parameter.