1 X-Ray Birefringence Imaging (XBI): A New Technique …
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phase is a consequence of reorientational dynamics of the guest molecules around
the tunnel axis, leading to a time-averaged projection of the C–Br bond vector along
this axis. For this motion, the actual orientational distribution of each C–Br bond is
described by a cone with semi-angle ca. 35.3° (Fig. 1.13c) and with the cone axis
parallel to the tunnel axis. The relative populations of different C–Br bond orientations on the cone are not necessarily equal, but at a given site along the tunnel axis,
the local environment experienced by the guest due to interaction with the host structure is described by a potential with approximately 6-fold rotational symmetry; thus,
the distribution of orientations of the C–Br vectors on the cone exhibits approximate
6-fold symmetry. For this orientational distribution, the resultant C–Br bond vector
is essentially parallel to the tunnel axis, representing the effective (time-averaged)
C–Br bond orientation that defines the X-ray optic axis for XBI. Thus, both 1,8DBrO/urea and 1,10-DBrD/urea exhibit sinusoidal variation of X-ray intensity as a
function of χ and essentially no variation of X-ray intensity as a function of φ. While
we have focused on the behavior of 1,8-DBrO/urea and 1,10-DBrD/urea in the HT
phase, XBI studies of these materials in the LT phase have also been reported [24].
The XBI behavior observed for 1,8-DBrO/urea and 1,10-DBrD/urea demonstrates
that, for materials undergoing anisotropic molecular dynamics, the effective X-ray
optic axis is the time-averaged resultant of the orientational distribution of the
C–Br bonds, which represents a basis for the rationalization of XBI behavior of
other materials in which the molecules undergo anisotropic dynamic processes.
1.5 Concluding Remarks and Future Prospects
As demonstrated by the results presented above, the XBI technique enables spatially
resolved mapping of the orientational properties of specific types of molecule and/or
bond in materials. Although several of the samples in these early studies were single
crystals, there is no requirement for crystallinity as X-ray birefringence is sensitive to local molecular orientations; thus, XBI could be applied to any material
(including liquid phases, liquid crystals, amorphous solids, or molecular assemblies
on surfaces) with an anisotropic distribution of molecular orientations. XBI can also
be exploited for spatially resolved analysis of orientationally distinct domains in
materials (see Fig. 1.7), yielding information on domain sizes, the orientational relationships between domains, and the nature of domain boundaries. Furthermore, as
XBI is a full-field imaging technique in which the entire image is recorded simultaneously, XBI data can be measured quickly (typical exposure times for the XBI
images shown here were around 1–5 s). Clearly, there are significant opportunities
to carry out in situ XBI studies of physical or chemical processes as a function of
time, with time resolution of the order of seconds.
Our ongoing research to further develop and apply the XBI technique is extending
the initial studies described above by investigating a significantly wider range of
materials (including those for which elements other than bromine are selected
as the X-ray absorbing element). Given the utility of XBI as a technique for
25
phase is a consequence of reorientational dynamics of the guest molecules around
the tunnel axis, leading to a time-averaged projection of the C–Br bond vector along
this axis. For this motion, the actual orientational distribution of each C–Br bond is
described by a cone with semi-angle ca. 35.3° (Fig. 1.13c) and with the cone axis
parallel to the tunnel axis. The relative populations of different C–Br bond orientations on the cone are not necessarily equal, but at a given site along the tunnel axis,
the local environment experienced by the guest due to interaction with the host structure is described by a potential with approximately 6-fold rotational symmetry; thus,
the distribution of orientations of the C–Br vectors on the cone exhibits approximate
6-fold symmetry. For this orientational distribution, the resultant C–Br bond vector
is essentially parallel to the tunnel axis, representing the effective (time-averaged)
C–Br bond orientation that defines the X-ray optic axis for XBI. Thus, both 1,8DBrO/urea and 1,10-DBrD/urea exhibit sinusoidal variation of X-ray intensity as a
function of χ and essentially no variation of X-ray intensity as a function of φ. While
we have focused on the behavior of 1,8-DBrO/urea and 1,10-DBrD/urea in the HT
phase, XBI studies of these materials in the LT phase have also been reported [24].
The XBI behavior observed for 1,8-DBrO/urea and 1,10-DBrD/urea demonstrates
that, for materials undergoing anisotropic molecular dynamics, the effective X-ray
optic axis is the time-averaged resultant of the orientational distribution of the
C–Br bonds, which represents a basis for the rationalization of XBI behavior of
other materials in which the molecules undergo anisotropic dynamic processes.
1.5 Concluding Remarks and Future Prospects
As demonstrated by the results presented above, the XBI technique enables spatially
resolved mapping of the orientational properties of specific types of molecule and/or
bond in materials. Although several of the samples in these early studies were single
crystals, there is no requirement for crystallinity as X-ray birefringence is sensitive to local molecular orientations; thus, XBI could be applied to any material
(including liquid phases, liquid crystals, amorphous solids, or molecular assemblies
on surfaces) with an anisotropic distribution of molecular orientations. XBI can also
be exploited for spatially resolved analysis of orientationally distinct domains in
materials (see Fig. 1.7), yielding information on domain sizes, the orientational relationships between domains, and the nature of domain boundaries. Furthermore, as
XBI is a full-field imaging technique in which the entire image is recorded simultaneously, XBI data can be measured quickly (typical exposure times for the XBI
images shown here were around 1–5 s). Clearly, there are significant opportunities
to carry out in situ XBI studies of physical or chemical processes as a function of
time, with time resolution of the order of seconds.
Our ongoing research to further develop and apply the XBI technique is extending
the initial studies described above by investigating a significantly wider range of
materials (including those for which elements other than bromine are selected
as the X-ray absorbing element). Given the utility of XBI as a technique for