X-Ray Reflectivity From the Surface of a Liquid

8/3/2019 X-Ray Reflectivity From the Surface of a Liquid

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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



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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



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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



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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


.(1)


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High-resolution scan


TTNA=0.40C


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Low-resolution signals


TTNA=0.011C - plussesTTNA=0.164C - crossesTTNA=1.105C -circles


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Transverse out-of-plane scans


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

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