20
K. D. M. Harris et al.
XBI at the Br K-edge depends on the resultant direction of the C–Br bonds, the XBI
behavior for the nematic phase indicates a high degree of molecular orientational
ordering, with a resultant C–Br bond orientation parallel to the magnetic field.
The XBI data for the smectic A phase (184 °C; Fig. 1.10c) also exhibit a sinusoidal
variation in X-ray intensity as a function of χ (Fig. 1.11). Significantly, the maximum
intensity (at χ = 45° and χ = –45°) is higher for the smectic A phase than the nematic
phase, indicating that the smectic A phase has a higher degree of ordering of the C–Br
bond orientations (i.e., a narrower orientational distribution) in the direction of the
magnetic field, as expected for a more ordered phase that has partial translational
ordering.
The type of XBI experiment described above in which the orientation of the
sample assembly is changed systematically by variation of χ at fixed temperature
can be problematic in the case of liquid crystals, as the domain structure can change
suddenly and unpredictably on changing the sample orientation due to the fluid nature
of these phases under gravity. Under these circumstances, it can be difficult to extract
reliable information on the characteristic dependence of X-ray intensity as a function
of χ for the different liquid crystal phases.
A more reliable method to explore differences in the degree of ordering between
different liquid crystal phases is to record the XBI images with the orientation of
the magnetic field fixed at χ = 45° while scanning through the temperature range of
interest. Results from this type of experiment are shown in Fig. 1.12, with the XBI
data recorded on decreasing temperature from 218 °C (isotropic liquid) to 108 °C
(crystalline phase) at a rate of 1 °C min
−1 , with the XBI images recorded continuously
on cooling (time per image, 5 s). At the highest temperature, the intensity is very low
as a result of the isotropic distribution of molecular orientations in the isotropic liquid
phase. On decreasing temperature, the intensity increases substantially between 216
and 205 °C, representing the transition from the isotropic liquid into orientationally
ordered phases (from Iso → N → SmA). Figure 1.12 (top part) shows the evolution
of the X-ray intensity measured from the XBI images as a function of temperature.
Between 216 and 205 °C, the data show a “first-order” change in intensity at the
clearing point as the nematic phase forms, after which there is a small inflection
over the approximate temperature range 215–211 °C (corresponding to the intensity
range from ca. 0.2 to 0.4). The fact that the sharp rise in intensity between 216 and
205 °C covers a significantly wider temperature range than the Iso → N → SmA
events observed by DSC and optical microscopy may reflect a combination of the
temperature gradient across the sample plus the kinetics of alignment in the presence of the magnetic field. As temperature decreases within the SmA phase, the
intensity increases gradually until a visible transition to the SmB phase is observed
from a further sharp (although relatively small) increase in intensity, followed by a
significant decrease in intensity upon crystallization.
The orientational order in liquid crystal phases is usually quantified by the orientational order parameter, S =
1 / 2 (3 cos
2
θ − 1)
, where θ is the angle between the
director and the individual long molecular axes. The value of S is often determined
by measuring optical birefringence, and it is clear that the X-ray intensity measured
in the XBI data is also related to the order parameter S. While our interpretations of
K. D. M. Harris et al.
XBI at the Br K-edge depends on the resultant direction of the C–Br bonds, the XBI
behavior for the nematic phase indicates a high degree of molecular orientational
ordering, with a resultant C–Br bond orientation parallel to the magnetic field.
The XBI data for the smectic A phase (184 °C; Fig. 1.10c) also exhibit a sinusoidal
variation in X-ray intensity as a function of χ (Fig. 1.11). Significantly, the maximum
intensity (at χ = 45° and χ = –45°) is higher for the smectic A phase than the nematic
phase, indicating that the smectic A phase has a higher degree of ordering of the C–Br
bond orientations (i.e., a narrower orientational distribution) in the direction of the
magnetic field, as expected for a more ordered phase that has partial translational
ordering.
The type of XBI experiment described above in which the orientation of the
sample assembly is changed systematically by variation of χ at fixed temperature
can be problematic in the case of liquid crystals, as the domain structure can change
suddenly and unpredictably on changing the sample orientation due to the fluid nature
of these phases under gravity. Under these circumstances, it can be difficult to extract
reliable information on the characteristic dependence of X-ray intensity as a function
of χ for the different liquid crystal phases.
A more reliable method to explore differences in the degree of ordering between
different liquid crystal phases is to record the XBI images with the orientation of
the magnetic field fixed at χ = 45° while scanning through the temperature range of
interest. Results from this type of experiment are shown in Fig. 1.12, with the XBI
data recorded on decreasing temperature from 218 °C (isotropic liquid) to 108 °C
(crystalline phase) at a rate of 1 °C min
−1 , with the XBI images recorded continuously
on cooling (time per image, 5 s). At the highest temperature, the intensity is very low
as a result of the isotropic distribution of molecular orientations in the isotropic liquid
phase. On decreasing temperature, the intensity increases substantially between 216
and 205 °C, representing the transition from the isotropic liquid into orientationally
ordered phases (from Iso → N → SmA). Figure 1.12 (top part) shows the evolution
of the X-ray intensity measured from the XBI images as a function of temperature.
Between 216 and 205 °C, the data show a “first-order” change in intensity at the
clearing point as the nematic phase forms, after which there is a small inflection
over the approximate temperature range 215–211 °C (corresponding to the intensity
range from ca. 0.2 to 0.4). The fact that the sharp rise in intensity between 216 and
205 °C covers a significantly wider temperature range than the Iso → N → SmA
events observed by DSC and optical microscopy may reflect a combination of the
temperature gradient across the sample plus the kinetics of alignment in the presence of the magnetic field. As temperature decreases within the SmA phase, the
intensity increases gradually until a visible transition to the SmB phase is observed
from a further sharp (although relatively small) increase in intensity, followed by a
significant decrease in intensity upon crystallization.
The orientational order in liquid crystal phases is usually quantified by the orientational order parameter, S =
1 / 2 (3 cos
2
θ − 1)
, where θ is the angle between the
director and the individual long molecular axes. The value of S is often determined
by measuring optical birefringence, and it is clear that the X-ray intensity measured
in the XBI data is also related to the order parameter S. While our interpretations of