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.
Efficient polynomial analysis of magic-angle spinning sidebands and application to order parameter determination in anisotropic samples