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NEUTRON DIFFRACTION FROM HOLOGRAPHIC
POLYMER-DISPERSED LIQUID CRYSTALS
I. Drevenšek-Olenika, M. A. Ellabbanb, M. Fallyb, K. P. Pranzasc J. Vollbrandtc
aFaculty
of Mathematics and Physics, University of Ljubljana, Jadranska 19,
and J. Stefan Institute, Jamova 39, Ljubljana, SI 1001, Slovenia
bNonlinear Physics Group, Faculty of Physics, University of Vienna, Boltzmanngasse 5,
Vienna, A-1090, Austria
cInstitute for Materials Research, GKSS-Research Center Geesthacht GmbH, PO Box 1160,
Geesthacht, 21494, Germany
NEUTRON PHYSICS WITH
PHOTOREFRACTIVE MATERIALS
• 1990 - a beam of cold neutrons (0.5 nm < B < 5 nm) was for the first time diffracted
from a periodic structure fabricated by optical holographic patterning
(R. A. Rupp et al., Phy. Rev. Lett. 64, 301 (1990))
Photo-neutron-refractive (PNR) effect = optical illumination-induced
modifications of the photosensitive material cause refractive index changes for
neutrons.
PNR effect provides:
• Structural characterization of holographic media on the nanoscale
• Convenient way for fabrication of various neutron-optical devices for cold and
ultracold neutrons (beam splitters, mirrors, lenses, interferometers, ...)
NEUTRON OPTICS
Coherent elastic scattering of cold neutrons with wavelengths of 0.5 nm < n < 5 nm,
can be described rigorously by a one-body, time-independent Schrödinger equation,
which can be expressed as:

2

 nn ( x)k0    0, k0 
2


2mE / h2  2 / n ,
where the refractive index for neutrons is given as:
nn ( x )  1 
V ( x)  V ( x) 
 1 

E
2
E


.
Nuclear potential V(x) is usually replaced by a series of Fermi pseudopotentials:
h2
h2 
V ( x) 
 b j ( x  y j )  2m b ( x)
2m j
,
where bj is the bound coherent scattering length of a nucleus j located at the site yj,
and b(x) is the so-called coherent scattering length density. Consequently
 2n  
nn ( x)  1  
b ( x) 
2



.
By averaging over the “unit cell” of the medium one can take b  ( x)  [b N ]( x) .
NEUTRON DIFFRACTION
Medium with sinusoidal modification of b.
nn ( x)  n0 n  n1n cos( K g x)
Kg=| Kg |=2/ = grating vector

B
Bragg angle: Bn=sin-1(n/2)
2n
2n 
n1n 
(b N ) 
b1
2
2
ANGULAR DEPENDENCE OF
DIFFRACTED INTENSITY
Diffraction efficiency  = Id/Iin : two wave coupling approximation (H. Kogelnik, 1969)
= n1nd/(cos)
Id
sin 2  2   2
 ( ,  ) 
1   2 / 2
d

grating strength
= d/
deviation from Bragg angle
B
Iin


Diffraction efficiency
1.0
1.0 (*/2)
0.8
0.6
0.4
0.2
0.8

0.6
0.4
0.2
0.0
-20
-10
0
10
units)
 (arb. 
20
The measured () (rocking curve) is the convolution of (,) with angular and
wavelength distributions of the incident neutron beam. (M. Fally, Appl. Phys. B 75, 405-426 (2002))
OUR HPDLC SAMPLES
1D gratings fabricated from UV curable emulsion:
• 55 wt% of the LC mixture (TL203, Merck),
• 33 wt% of the prepolymer (PN393, Nematel),
• 12 wt% of the 1,1,1,3,3,3,3-Hexafluoroisopropyl acrylate
(HFIPA, Sigma-Aldrich).
I. Drevenšek Olenik, M. E. Sousa, A. K. Fontecchio, G. P. Crawford, M. Čopič:
Phys. Rev. E, 69, 051703-1-9 (2004).
• Standard glass cells with 50 or 100 m thick spacers,
• Exposure: Ar laser, UV = 351 nm , 2 beams with j ~ 10 mW/cm2
• Unslanted transmission grating,  = 0.43, 0.56, 1.0, 1.2 m,
• Postcuring: Exposure to one beam for ~ 5 min.
SEM image of an “opened” sample
Diffraction pattern observed for
optical beam with O=543 nm
at normal incidence.
OPTICAL DIFFRACTION IN THE NEMATIC PHASE
I-1
I-2
I0
I+1
I+2
Iin
Grating  = 1.2 m:
Angular dependence of the
1st order diffracted intensities.
• Strong difference between
p- and s- polarized beams.
• Overmodulated diffraction for
p-polarized light.
OPTICAL DIFFRACTION IN THE ISOTROPIC PHASE
Grating  = 1.2 m
n( x)  n0 op  n1op cos( K g x)
sin 2  2   2
 ( ,  ) 
1   2 / 2
 = n1opd/(cos),  = d/
The fit gives:
s =1.89 0.03 , p = 1.840.03
d = 30.50.4 m ,
n0op = 1.520.01 and n1op = 0.0110.001
Accordingly to the sample composition
max possible n1,op=0.038.
I. Drevensek-Olenik, M. Fally, M. Ellaban,
Phys. Rev. E 74, 021707 (2006).
NEUTRON DIFFRACTION EXPERIMENTS
• SANS-2 instrument at the Geesthacht Neutron Facility (GeNF)
• Beam size: circular spot with 5 mm diameter
• Central neutron wavelengths used: n = 1,16 nm; n = 1,96 nm
• Wavelength spread: ( n /n)= 10%
• Full collimation distance of 40 m was used (angular spread ~0.5 mrad)
• Maximum detector distance of 21 m was used.
• 2D decetor with 256x256 pixels (2.2 x 2.2 mm2)
• All measurements were done at 22oC
NEUTRON DIFFRACTION IN THE NEMATIC PHASE
Grating  = 1.2 m
• Diffraction pattern for n = 1,96 nm
measured at =0o.
• The diffraction efficiency of the 1st diffraction
orders is around 10% !!!
• Diffraction peaks up to the 2nd order are visible.
(non-deuterated sample!!)
ANGULAR DEPENDENCE of NEUTRON DIFFRACTION
Sample 10g
Sample 10f
n = 1,16 nm
Bn=sin-1(n/2)=0.48 mrad
sin 2  2   2
Red line = fit to  ( ,  ) 
1   2 / 2
From the fit it follows:
n1n= (2.120.05)10-6, d=30 m
=> b1 = (9.890.26)1012 m-2
The corresponding modulation of the coherent scattering length density b1 is two
orders of magnitude larger than in the best PNR materials reported up to now!!
b1 = (bN), due to phase separation of the constituent compounds
(b) can be large even if (N) is relatively small !!!
M. Fally, I. Drevensek-Olenik, M. Ellaban, K. P. Pranzas, J. Vollbrandt,
Phys. Rev. Lett. 97, 167803 (2006).
WHAT ARE THE BENEFITS ?
From the info on chemical composition of our samples we calculated n0 ~ (1–7·10-5).
While we detected n1n ~ 6.3 ·10-6 (for n = 1.96 nm).
This means that in our HPDLC gratings 10% variation of the V(x) for neutrons was induced by
optical holographic patterning.
For observed n1n the value of  = 100% can be reached by grating thickness d = 156 m !!!
Low thickness brings important advantages in construction of neutron optical devices:
• low level of incoherent scattering (no need for material deuteration = low price)
• alignment procedures for different neutron-optical elements become very simple!!
INCREASING GRATING THICKNESS
Grating  = 1 m, spacers dS = 50 and 100 m
cell thickness dS
50 m
100 m
n.d. efficiency 
grating thickness d
36 4 m
87 6 m
0.9 %
0.5 %
ref. ind. modulation n1n (1.16 nm)
1.0 ·10-6
0.3 ·10-6
Increased sample thickness resulted in lower refractive index modulation for neutrons ?!?
Besides this an anusual double Bragg peak was observed.
Diffraction efficiency
0.006
+1st order
-1st order
0.005
0.004
Possible explanation
0.003
0.002
0.001
0.000
-0.06
According to two beam coupling theory:
= at =/d=0.01 rad.
So we actually see 2 separate Bragg peaks.
-0.04
-0.02
0.00
0.02
Angle (rad)
0.04
0.06
DECREASING GRATING PITCH
Grating  = 0.56 m, spacers dS = 50 m (d = 30 5 m).
Diffraction efficiency (%)
1.0
Kogelnik
Gaussian
-1st order
0.8
Lorentzian
0.6
0.4
0.2
n1n ~ 1.1 ·10-6 (for n = 1.16 nm).
0.0
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
Angle [rad]
Decreasing grating pitch resulted in smearing and broadening of the Bragg peak, which is
attributed to structural inhomogeneities.
CONTRAST VERSUS GRATING PITCH
-6
n1n (at n = 1.16 nm)
2.5x10
Our acrylate-based HPDLC mixture is
very convenient for fabricating structures
with  > 1 m, but less suitable for
submicron patterning.
-6
2.0x10
-6
1.5x10
nn ( x)  n0 n  n1n cos( K g x)
-6
1.0x10
-7
5.0x10
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
 (micrometers)
AFM images of polymer matrix
 = 0.43 m
0.56 m
1.0 m
FUTURE PERSPECTIVES
• Probing of other sample compositions (different polymers, LCs, ...)
• (Re)filling of the grating structures with high contrast materials (D2O, ...)
• Study of photopolymerization kinetics of H-PDLCs by neutron scattering in-situ
• Synchronous probing of optical and neutron refractive properties
• Investigations of sample morphology on the nanoscale
• Investigations of structural modifications induced by external fields
• Fabrication of 2D and 3D grating structures for neutrons
• Assembling of neutron-optical elements
HOLONS-setup at GeNF
M. Fally, C. Pruner, R.A. Rupp, G. Krexner, Neutron Physics with Photorefractive Materials in Springer Series
of Optical Sciences 115, eds. P. Gunter and J.-P. Huignard, Springer Verlag, 2007.
CONCLUSIONS
• Photopolymerization-induced phase separation of the constituent components in
H-PDLCs causes a huge variation of refractive index for light as well as for neutrons.
• H-PDLC transmission gratings with the thickness of only few tens of micrometers act
as extremely efficient gratings for neutrons.
• The light induced refractive index-modulation for neutrons in HPDLCs is two orders
of magnitude larger than found in the best PNR materials probed up to now.
• These features make H-PDLCs very
promising candidate for fabrication
of neutron-optical devices
• Our results also demonstrate that
neutron diffraction is a very
convenient tool to investigate
structural properties of the HPDLCs.
C. Pruner et al., Nuclear Instruments and Methods in
Physics Research Section A 560, 598 (2006).
PARTICIPATING RESEARCHERS
M. A. Ellabban
H. Eckerlebe, M. Fally, M. Bichler
P. K. Pranzas
I. Drevensek Olenik
J. Vollbrandt
____________________________________________________________________________________________
We acknowledge the financial support of ÖAD and Slovenian Research Agency
(bilateral projects SI-A4/0708 and SI-AT/07-08-004),
the Austrian Science fund FWF (project P-18988),
and support of the GKSS–Research Center Geesthacht.