Chemistry Reference
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tion is approached from above, the smectic correlation length does not diverge any
more as observed normally, but instead reaches a finite value. Upon cooling through
the smectic phase this value saturates at a length scale of the order of 100 nm
the correlation length is not limited by some sort of effective “pore size” as if the
system has simply been broken up in small pieces. It is rather a result of competition
between the randomizing effect of the confinement and the smectic elasticity.
Ordering effects and phase transitions in imperfect crystals are strongly influ-
enced by the types of defects and their mobility (see, for example, [
121
]). If point
defects have a high enough mobility to adjust (rearrange) to changing long-range
order, their presence has no qualitative effect on the large-scale properties of the
medium. Such weak “annealed disorder” causes only a finite renormalization of the
effective parameters of the ordered state, and the phase transition to a less-ordered
state remains sharp. In the case of “quenched disorder” the positions of the
impurities are fixed in space and time and they produce a much stronger effect.
Their effective field is linearly related to the order parameter and violates the
symmetry of the ordered state. Under these conditions, defects can destroy the
long-range-order in a 3D crystal, leading to a disordered state. Even weak quenched
disorder destroys translational order below four dimensions, resulting in exponen-
tially decaying positional correlations [
122
]. Under certain conditions a continuous
transition can occur to a state with the peculiar property of being a glass with many
metastable states and at the same time showing Bragg peaks as in conventional
280
bulk nematic-smectic A
transition
T
NA
= 33.7 °C
240
200
ξ
sal
= 216 Å
ξ
||
160
smectic A
120
80
40
0
0
5
10
15
20
25
30
35
40
T(°C)
Fig. 10 X-ray correlation length, x, for the smectic layer order around the nematic-smectic-A
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