x-ray reflectivity from the surface of a liquid
TRANSCRIPT
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X-Ray Reflectivity from the Surface of a Liquid Crystal:
Surface Structure and Absolute Value of Critical Fluctuations
P. S. Pershan and J. Als-Nielsen
(Received 1 November 1983)
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AbstractX-ray reflectivity from the surface of a nematic liquid crystal is interpreted as the
coherent superposition of Fresnel reflection from the surface and Bragg reflection
from smectic order induced by the surface. Angular dependence of the Fresnel
effect yields information on surface structure. Measurement of the intensity of
diffuse critical scattering relative to the Fresnel reflection yields the absolute valueof the critical part of the density-density correlation function.
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Purposes
X-Ray Reflectivity from the Surface of a Liquid Crystal
To demonstrate that, with use of a synchrotron source, x-ray reflectivity from liquid
[Octyloxycyanobiphenyl OCB] surfaces is a practical technique for obtaining
structural information at the molecular level
To demonstrate that since the x-ray reflectivity can be calculated from the Fresnel
formulas, the ratio of the scattering from critical fluctuations in the nematic phase of
bulk 8OCB to the signal reflected from the surface yields the absolute value of the
critical part of the density-density correlation function
Similarly the absolute value of the surface-induced smectic order in the nematic
phase is also measured
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Experiments
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Schematic of the spectrometer geometry
=1.541.510.03
for low resolution20.732= 0.4
for high resolution
20.012= 0.03
X-Ray Reflectivity from the Surface of a Liquid Crystal
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High-resolution scan of the reflected intensity
from the surface of8OCB
K=1
Qz=Qo=0.1989
TTNA=0.05C
The calculated Fresnelreflection law
X-Ray Reflectivity from the Surface of a Liquid Crystal
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Displays the result of dividing
the data by the Fresnel reflection law
TTNA=0.05C - the solid lineTTNA=2.8C - open circlesTTNA=11.6C - crosses
K=Qz/Qo=1
X-Ray Reflectivity from the Surface of a Liquid Crystal
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Schematic shape of the full width at half maximum
for critical scattering from the bulk nematic phase0.5Qz/Qo=2/Qo ll(T)
ll(T) is the longitudinal correlation length of
the bulk nematic
X-Ray Reflectivity from the Surface of a Liquid Crystal
.(1)
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High-resolution scan
X-Ray Reflectivity from the Surface of a Liquid Crystal
TTNA=0.40C
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Low-resolution signals
X-Ray Reflectivity from the Surface of a Liquid Crystal
TTNA=0.011C - plussesTTNA=0.164C - crossesTTNA=1.105C -circles
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Transverse out-of-plane scans
X-Ray Reflectivity from the Surface of a Liquid Crystal
TTNA=0.796CKz=1.0
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Since and is essentially temperature independent.
The same is true for the five other materials for which published data exist. Thus the
absolute value of is a useful measure of the
absolute value of the critical part of the density-density correlation function.
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Summarize` demonstrated the utility of x-ray reflectivity to obtain information on fluid
surfaces
` demonstrated that since the Fresnel reflection laws can be applied to x-ray
wavelengths
` demonstrated for the 8OCB that the interference between densityoscillations localized at the surface and surface-induced smectic order that
decays into the bulk as exp(-z/ll)cos(Qoz) is responsible for the shape of
the peak at K=1
` obtained a value for the critical part of(r)
X-Ray Reflectivity from the Surface of a Liquid Crystal