NEUTRON DIFFRACTION FROM HOLOGRAPHIC POLYMER-DISPERSED LIQUID CRYSTALS

NEUTRON DIFFRACTION FROM HOLOGRAPHIC NEUTRON DIFFRACTION FROM HOLOGRAPHIC POLYMERPOLYMER--DISPERSED LIQUID CRYSTALSDISPERSED 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

NEUTRON PHYSICS WITH NEUTRON PHYSICS WITH PHOTOREFRACTIVE MATERIALSPHOTOREFRACTIVE MATERIALS

• 1990 - a beam of cold neutrons (0.5 nm < λB < 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 OPTICSNEUTRON OPTICSNEUTRON OPTICSCoherent elastic scattering of cold neutrons with wavelengths of 0.5 nm < λn < 5 nm, can be described rigorously by a one-body, time-independent Schrödinger equation, which can be expressed as:

( )( ) ( ) nn hmEkkxn λπ /2/2 ,0 )( 20202 ===Ψ+∇ ,where the refractive index for neutrons is given as:

−≈−=

xVxVxnn 2)(1)(1)(

.EENuclear potential V(x) is usually replaced by a series of Fermi pseudopotentials:

)(2

)(2

)(22

xbm

hyxbm

hxVj

jjρ

πδ

π=−= ∑ ,

where bj is the bound coherent scattering length of a nucleus j located at the site yj,and bρ(x) is the so-called coherent scattering length density. Consequently

−= )(

21)(

2

xbxn nnρ

πλ

By averaging over the “unit cell” of the medium one can take )]([)( xNbxb =ρ .

.

NEUTRON DIFFRACTIONNEUTRON DIFFRACTIONNEUTRON DIFFRACTION

θB

Medium with sinusoidal modification of bρ.

)cos()( 10 xKnnxn gnnn +=

Kg=| Kg |=2π/Λ = grating vectorΛρ

πλ

πλ

1

22

1 2)(

2bNbn nnn =∆=

Bragg angle: θBn=sin-1(λn/2Λ)

ANGULAR DEPENDENCE OF DIFFRACTED INTENSITY

ANGULAR DEPENDENCE OF ANGULAR DEPENDENCE OF DIFFRACTED INTENSITYDIFFRACTED INTENSITY

Diffraction efficiency η = Id/Iin : two wave coupling approximation (H. Kogelnik, 1969)

θB ∆θ

22

222

/1sin

),(νξ

ξνξνη

++

=

ν= πn1nd/(λcosθ)grating strength

ξ= ∆θπd/Λdeviation from Bragg angle

θ

-20 -10 0 10 200.0

0.2

0.4

0.6

0.8

1.0

(arb. units)

Diff

ract

ion

effic

ienc

y

∆α

1.0 (*π/2) 0.8 0.6 0.4 0.2

Iin

Id

θ

ν

d

Λ

The measured η(θ) (rocking curve) is the convolution of η(ν,ξ) with angular and wavelength distributions of the incident neutron beam. (M. Fally, Appl. Phys. B 75, 405-426 (2002))

OUR HPDLC SAMPLESOUR HPDLC SAMPLESOUR HPDLC SAMPLES1D 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 µm thick spacers,• Exposure: Ar laser, λUV = 351 nm , 2 beams with j ~ 10 mW/cm2• Unslanted transmission grating, Λ = 0.43, 0.56, 1.0, 1.2 µm,• Postcuring: Exposure to one beam for ~ 5 min.

SEM image of an “opened” sample

Diffraction pattern observed for optical beam with λO=543 nmat normal incidence.

OPTICAL DIFFRACTION IN THE NEMATIC PHASEOPTICAL DIFFRACTION IN THE NEMATIC PHASEOPTICAL DIFFRACTION IN THE NEMATIC PHASE

• Strong difference betweenp- and s- polarized beams.• Overmodulated diffraction for p-polarized light.

I0I-1 I+1I-2 I+2

IinGrating Λ = 1.2 µm:Angular dependence of the ±1st order diffracted intensities.

OPTICAL DIFFRACTION IN THE ISOTROPIC PHASEOPTICAL DIFFRACTION IN THE ISOTROPIC PHASEOPTICAL DIFFRACTION IN THE ISOTROPIC PHASE

Grating Λ = 1.2 µm

)cos()( 10 xKnnxn gopop +=

22

222

/1sin

),(νξ

ξνξνη

++

=

ν = πn1opd/(λcosθ), ξ = ∆θπd/Λ

The fit gives:νs =1.89 ±0.03 , νp = 1.84±0.03d = 30.5±0.4 µm ,

n0op = 1.52±0.01 and n1op = 0.011±0.001

Accordingly to the sample compositionmax possible n1,op=0.038.

I. Drevensek-Olenik, M. Fally, M. Ellaban,Phys. Rev. E 74, 021707 (2006).

NEUTRON DIFFRACTION EXPERIMENTSNEUTRON DIFFRACTION EXPERIMENTSNEUTRON DIFFRACTION EXPERIMENTS• SANS-2 instrument at the Geesthacht Neutron Facility (GeNF)• Beam size: circular spot with 5 mm diameter • Central neutron wavelengths used: λn = 1,16 nm; λn = 1,96 nm• Wavelength spread: (∆ λn /λn)= 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 PHASENEUTRON DIFFRACTION IN THE NEMATIC PHASENEUTRON DIFFRACTION IN THE NEMATIC PHASE

Grating Λ = 1.2 µm

• Diffraction pattern for λn = 1,96 nm measured at θ=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 DIFFRACTIONANGULAR DEPENDENCE of NEUTRON DIFFRACTIONANGULAR DEPENDENCE of NEUTRON DIFFRACTION

Sample 10f

Sample 10g

Red line = fit to 22222

/1sin

),(νξ

ξνξνη

++

=

From the fit it follows:n1n= (2.12±0.05)⋅10-6, d=30 µm=> b1ρ = (9.89±0.26)⋅1012 m-2

λn = 1,16 nmθBn=sin-1(λn/2Λ)=0.48 mrad

The corresponding modulation of the coherent scattering length density b1ρ is two orders of magnitude larger than in the best PNR materials reported up to now!!

b1ρ = ∆(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 ?WHAT ARE THE BENEFITS ?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 λn = 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 η = 100% can be reached by grating thickness d = 156 µm !!!

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 THICKNESSINCREASING GRATING THICKNESSINCREASING GRATING THICKNESSGrating Λ = 1 µm, spacers dS = 50 and 100 µmcell thickness dS n.d. efficiency η grating thickness d ref. ind. modulation n1n (1.16 nm)

50 µm 0.9 % 36 ±4 µm 1.0 ·10-6100 µm 0.5 % 87 ±6 µm 0.3 ·10-6

Increased sample thickness resulted in lower refractive index modulation for neutrons ?!?Besides this an anusual double Bragg peak was observed.

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.060.000

0.001

0.002

0.003

0.004

0.005

0.006

+1st order -1st order

Diff

ract

ion

effic

ienc

y

Angle (rad)

According to two beam coupling theory:ξ=π at ∆θ=Λ/d=0.01 rad. So we actually see 2 separate Bragg peaks.

Possible explanation

DECREASING GRATING PITCHDECREASING GRATING PITCHDECREASING GRATING PITCHGrating Λ = 0.56 µm, spacers dS = 50 µm (d = 30 ±5 µm).

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08

0.0

0.2

0.4

0.6

0.8

1.0

-1st order

Diff

ract

ion

effic

ienc

y (%

)

Angle [rad]

KogelnikGaussianLorentzian

Decreasing grating pitch resulted in smearing and broadening of the Bragg peak, which is attributed to structural inhomogeneities.

n1n ~ 1.1 ·10-6 (for λn = 1.16 nm).

CONTRAST VERSUS GRATING PITCHCONTRAST VERSUS GRATING PITCHCONTRAST VERSUS GRATING PITCH

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

5.0x10-7

1.0x10-6

1.5x10-6

2.0x10-6

2.5x10-6

n 1 (

at λ

n = 1

.16

nm)

Λ (micrometers)

n

Our acrylate-based HPDLC mixture is very convenient for fabricating structureswith Λ > 1 µm, but less suitable for submicron patterning.

)cos()( 10 xKnnxn gnnn +=

AFM images of polymer matrix

Λ = 0.43 µm 0.56 µm 1.0 µm

FUTURE PERSPECTIVESFUTURE PERSPECTIVESFUTURE PERSPECTIVES

HOLONS-setup at GeNF

• 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

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.

CONCLUSIONSCONCLUSIONSCONCLUSIONS• 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 H-PDLCs.

C. Pruner et al., Nuclear Instruments and Methods in Physics Research Section A 560, 598 (2006).

PARTICIPATING RESEARCHERSPARTICIPATING RESEARCHERSPARTICIPATING RESEARCHERS

M. A. Ellabban I. Drevensek OlenikH. Eckerlebe, M. Fally, M. Bichler

P. K. Pranzas 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.