Spin-label Order Parameter Calibrations for Slow Motion

Abstract

Abstract 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, $$2A_{\hbox{max} }$$ 2 A max and $$2A_{\hbox{min} }$$ 2 A min , of the outer and inner peaks on order parameter $$S_{zz}$$ S z z that depends on the diffusion coefficient $$D_{{{\text{R}} \bot }}$$ D R ⊥ which characterizes fluctuations of the long molecular axis. This results in empirical expressions for order parameter and isotropic hyperfine coupling: $$S_{zz} = s_{1} \times \left( {A_{\hbox{max} } - A_{\hbox{min} } } \right) - s_{o}$$ S z z = s 1 × A max - A min - s o and $$a_{o}^{{}} = \tfrac{1}{3}\left( {f_{\hbox{max} } A_{\hbox{max} } + f_{\hbox{min} } A_{\hbox{min} } } \right) + \delta a_{o}$$ a o = 1 3 f max A max + f min A min + δ a o , respectively. Values of the calibration constants $$s_{1}$$ s 1 , $$s_{\text{o}}$$ s o , $$f_{\hbox{max} }$$ f max , $$f_{\hbox{min} }$$ f min and $$\delta a_{o}$$ δ a o are given for different values of $$D_{{{\text{R}} \bot }}$$ D R ⊥ in fast and slow motional regimes. The calibrations are relatively insensitive to anisotropy of rotational diffusion $$(D_{{{\text{R}}//}} \ge D_{{{\text{R}} \bot }} )$$ ( D R / / ≥ D R ⊥ ) , and corrections are less significant for the isotropic hyperfine coupling than for the order parameter.